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  <doc>
    <id>6972</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-07-31</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimization of Capacity Expansion in Potential-driven Networks including Multiple Looping - A comparison of modelling approaches</title>
    <abstract language="eng">In commodity transport networks such as natural gas, hydrogen and water networks, flows arise from nonlinear potential differences between the nodes, which can be represented by so-called "potential-driven" network models. When operators of these networks face increasing demand or the need to handle more diverse transport situations, they regularly seek to expand the capacity of their network by building new pipelines parallel to existing ones ("looping"). &#13;
The paper introduces a new mixed-integer non-linear programming (MINLP) model and a new non-linear programming (NLP) model and compares these with existing models for the looping problem and related problems in the literature, both theoretically and experimentally.&#13;
On this basis, we give recommendations about the circumstances under which a certain model should be used. In particular, it turns out that one of our novel models outperforms the existing models.&#13;
Moreover, the paper is the first to include the practically relevant option that a particular pipeline may be looped several times.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-69726</identifier>
    <identifier type="doi">10.1007/s00291-021-00648-7</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-69726</enrichment>
    <author>Ralf Lenz</author>
    <submitter>Ralf Lenz</submitter>
    <author>Kai-Helge Becker</author>
    <series>
      <title>ZIB-Report</title>
      <number>18-44</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>OR in energy</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Network expansion</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>MINLP</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="lenz">Lenz, Ralf</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="projects" number="ECMATH-MI10">ECMATH-MI10</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6972/ZR_18_44.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/6972/ZR_18_44_revised.pdf</file>
  </doc>
  <doc>
    <id>7041</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-09-15</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Open Newton Method for Piecewise Smooth Systems</title>
    <abstract language="eng">Recent research has shown that piecewise smooth (PS) functions can be approximated by piecewise linear functions with second order error in the distance to&#13;
a given reference point. A semismooth Newton type algorithm based on successive application of these piecewise linearizations was subsequently developed&#13;
for the solution of PS equation systems. For local bijectivity of the linearization&#13;
at a root, a radius of quadratic convergence was explicitly calculated in terms&#13;
of local Lipschitz constants of the underlying PS function. In the present work&#13;
we relax the criterium of local bijectivity of the linearization to local openness.&#13;
For this purpose a weak implicit function theorem is proved via local mapping&#13;
degree theory. It is shown that there exist PS functions f:IR^2 --&gt; IR^2 satisfying the weaker&#13;
criterium where every neighborhood of the root of f contains a point x such that&#13;
all elements of the Clarke Jacobian at x are singular. In such neighborhoods&#13;
the steps of classical semismooth Newton are not defined, which establishes&#13;
the new method as an independent algorithm. To further clarify the relation between a PS function and its piecewise linearization,&#13;
several statements about structure correspondences between the two are proved. &#13;
Moreover, the influence of the specific representation of the local piecewise linear models&#13;
on the robustness of our method is studied.&#13;
 An example application from cardiovascular mathematics is given.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-70418</identifier>
    <author>Manuel Radons</author>
    <submitter>Tom Streubel</submitter>
    <author>Lutz Lehmann</author>
    <author>Tom Streubel</author>
    <author>Andreas Griewank</author>
    <series>
      <title>ZIB-Report</title>
      <number>18-43</number>
    </series>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="enernet">Energy Network Optimization</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7041/Open_Newton.pdf</file>
  </doc>
  <doc>
    <id>6963</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-07-25</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">ASTS Orientations on Undirected Graphs: Structural analysis and enumeration</title>
    <abstract language="eng">All feasible flows in potential-driven networks&#13;
induce an orientation on the undirected graph underlying the network.&#13;
Clearly, these orientations must satisfy two conditions: they are acyclic and there are no "dead ends" in the network, i.e. each source requires outgoing flows, each sink requires incoming flows, and each transhipment vertex requires both an incoming and an outgoing flow. In this paper we will call orientations that satisfy these conditions acyclic source-transhipment-sink orientations (ASTS-orientation) and study their structure. In particular, we characterize graphs that allow for such an orientation, describe a way to enumerate all possible ASTS-orientations of a given graph, present an algorithm to simplify and decompose a graph before such an enumeration and shed light on the role of zero flows in the context of ASTS-orientations.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-69632</identifier>
    <author>Kai-Helge Becker</author>
    <submitter>Benjamin Hiller</submitter>
    <author>Benjamin Hiller</author>
    <series>
      <title>ZIB-Report</title>
      <number>18-31</number>
    </series>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="projects" number="ECMATH-MI10">ECMATH-MI10</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6963/ZR-18-31ZIB.pdf</file>
  </doc>
  <doc>
    <id>6962</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-07-25</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Improving relaxations for potential-driven network flow problems via acyclic flow orientations</title>
    <abstract language="eng">The class of potential-driven network flow problems provides important models for a range of infrastructure networks. For real-world applications, they need to be combined with integer&#13;
models for switching certain network elements, giving rise to hard-to-solve MINLPs. We observe that on large-scale real-world meshed networks the usually employed relaxations are rather weak due to cycles in the network.&#13;
&#13;
We propose acyclic flow orientations as a combinatorial relaxation of feasible solutions of potential-driven flow problems and show how they can be used to strengthen existing relaxations. First computational results indicate that the strengthend model is much tighter than the original relaxation, thus promising a computational advantage.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-69622</identifier>
    <author>Benjamin Hiller</author>
    <submitter>Benjamin Hiller</submitter>
    <author>Kai-Helge Becker</author>
    <series>
      <title>ZIB-Report</title>
      <number>18-30</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>potential-driven network flows</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>acyclic orientations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>flow orientations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>MINLPs</value>
    </subject>
    <collection role="ccs" number="G.">Mathematics of Computing</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="projects" number="ECMATH-MI10">ECMATH-MI10</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6962/ZR-18-30ZIB.pdf</file>
  </doc>
  <doc>
    <id>6947</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-07-16</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Exploiting structure in non-convex quadratic optimization</title>
    <abstract language="eng">The amazing success of computational mathematical optimization over the last decades has been driven more by insights into mathematical structures than by the advance of computing technology. In this vein, we address applications, where nonconvexity in the model poses principal difficulties.&#13;
&#13;
This paper summarizes the dissertation of Jonas Schweiger for the occasion of the GOR dissertation award 2018. We focus on the work on non-convex quadratic programs and show how problem specific structure can be used to obtain tight relaxations and speed up Branch&amp;Bound methods. Both a classic general QP and the Pooling Problem as an important practical application serve as showcases.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-69476</identifier>
    <author>Jonas Schweiger</author>
    <submitter>Jonas Schweiger</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>18-35</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Nonconvexity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Quadratic Programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Relaxations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Cutting Planes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Standard Quadratic Programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Pooling Problem</value>
    </subject>
    <collection role="msc" number="90C20">Quadratic programming</collection>
    <collection role="msc" number="90C26">Nonconvex programming, global optimization</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="schweiger">Schweiger, Jonas</collection>
    <collection role="institutes" number="enernet">Energy Network Optimization</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6947/ZR-18-35.pdf</file>
  </doc>
  <doc>
    <id>6948</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-07-17</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Sweep-Plane Algorithm for the Computation of the Volume of a Union of Polytopes</title>
    <abstract language="eng">Optimization models often feature disjunctions of polytopes as&#13;
submodels. Such a disjunctive set is initially (at best) relaxed to&#13;
its convex hull, which is then refined by branching.&#13;
&#13;
To measure the error of the convex relaxation, the (relative)&#13;
difference between the volume of the convex hull and the volume of the&#13;
disjunctive set may be used. This requires a method to compute the&#13;
volume of the disjunctive set. Naively, this can be done via&#13;
inclusion/exclusion and leveraging the existing code for the volume&#13;
of polytopes. However, this is often inefficient.&#13;
&#13;
We propose a revised variant of an old algorithm by Bieri and Nef&#13;
(1983) for this purpose. The algorithm uses a sweep-plane to&#13;
incrementally calculate the volume of the disjunctive set as a&#13;
function of the offset parameter of the sweep-plane.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-69489</identifier>
    <author>Lovis Anderson</author>
    <submitter>Lovis Anderson</submitter>
    <author>Benjamin Hiller</author>
    <series>
      <title>ZIB-Report</title>
      <number>18-37</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Disjunctive Programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Volume Algorithm</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Union of Polytopes</value>
    </subject>
    <collection role="ccs" number="G.">Mathematics of Computing</collection>
    <collection role="pacs" number="00.00.00">GENERAL</collection>
    <collection role="msc" number="49-XX">CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="TRR154-A04">TRR154-A04</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <thesisPublisher>Zuse Institute Berlin (ZIB)</thesisPublisher>
    <file>https://opus4.kobv.de/opus4-zib/files/6948/ZR-18-37.pdf</file>
  </doc>
  <doc>
    <id>6782</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-03-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Strong Convex Nonlinear Relaxations of the Pooling Problem</title>
    <abstract language="eng">We investigate new convex relaxations for the pooling problem, a classic nonconvex production planning problem in which input materials are mixed in intermediate pools, with the outputs of these pools further mixed to make output products meeting given attribute percentage requirements. Our relaxations are derived by considering a set which arises from the formulation by considering a single product, a single attibute, and a single pool. The convex hull of the resulting nonconvex set is not polyhedral. We derive valid linear and convex nonlinear inequalities for the convex hull, and demonstrate that different subsets of these inequalities define the convex hull of the nonconvex set in three cases determined by the parameters of the set. Computational results on literature instances and newly created larger test instances demonstrate that the inequalities can significantly strengthen the convex relaxation of the pq-formulation of the pooling problem, which is the relaxation known to have the strongest bound.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-67824</identifier>
    <author>James Luedtke</author>
    <submitter>Jonas Schweiger</submitter>
    <author>Claudia D'Ambrosio</author>
    <author>Jeff Linderoth</author>
    <author>Jonas Schweiger</author>
    <series>
      <title>ZIB-Report</title>
      <number>18-12</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Pooling Problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Relaxation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Valid Inequalities</value>
    </subject>
    <collection role="msc" number="90C20">Quadratic programming</collection>
    <collection role="msc" number="90C26">Nonconvex programming, global optimization</collection>
    <collection role="msc" number="90C35">Programming involving graphs or networks [See also 90C27]</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="schweiger">Schweiger, Jonas</collection>
    <collection role="institutes" number="enernet">Energy Network Optimization</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6782/ZR-18-12.pdf</file>
  </doc>
  <doc>
    <id>6817</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-03-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Analysis of operating modes of complex compressor stations</title>
    <abstract language="eng">We consider the modeling of operation modes for complex compressor stations (i.e., ones with several in- or outlets) in gas networks. In particular, we propose a refined model that allows to precompute tighter relaxations for each operation mode. These relaxations may be used to strengthen the compressor station submodels in gas network optimization problems. We provide a procedure to obtain the refined model from the input data for the original model. This procedure is based on a nontrivial reduction of the graph representing the gas flow through the compressor station in an operation mode.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-68179</identifier>
    <author>Benjamin Hiller</author>
    <submitter>Benjamin Hiller</submitter>
    <author>René Saitenmacher</author>
    <author>Tom Walther</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-65</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>bound tightening</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>flow patterns</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>model reformulation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>multi-way compressor station</value>
    </subject>
    <collection role="ccs" number="J.">Computer Applications</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="TRR154-A04">TRR154-A04</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6817/ZR-17-65.pdf</file>
  </doc>
  <doc>
    <id>6780</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-03-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Strong Convex Nonlinear Relaxations of the Pooling Problem: Extreme Points</title>
    <abstract language="eng">We investigate new convex relaxations for the pooling problem, a classic nonconvex production planning problem in which products are mixed in intermediate pools in order to meet quality targets at their destinations. In this technical report, we characterize the extreme points of the convex hull of our non-convex set, and show that they are not finite, i.e., the convex hull is not polyhedral. This analysis was used to derive valid nonlinear convex inequalities and show that, for a specific case, they characterize the convex hull of our set. The new valid inequalities and computational results are presented in ZIB Report 18-12.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-67801</identifier>
    <author>James Luedtke</author>
    <submitter>Jonas Schweiger</submitter>
    <author>Claudia D'Ambrosio</author>
    <author>Jeff Linderoth</author>
    <author>Jonas Schweiger</author>
    <series>
      <title>ZIB-Report</title>
      <number>18-13</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Pooling Problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Relaxation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Extreme Points</value>
    </subject>
    <collection role="msc" number="90C20">Quadratic programming</collection>
    <collection role="msc" number="90C26">Nonconvex programming, global optimization</collection>
    <collection role="msc" number="90C35">Programming involving graphs or networks [See also 90C27]</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="schweiger">Schweiger, Jonas</collection>
    <collection role="institutes" number="enernet">Energy Network Optimization</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6780/ZR-18-13.pdf</file>
  </doc>
  <doc>
    <id>8145</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2021-02-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Tight Convex Relaxations for the Expansion Planning Problem</title>
    <abstract language="eng">Secure energy transport is considered as highly relevant for the basic infrastructure of nowadays society and economy. To satisfy increasing demands and to handle more diverse transport situations, operators of energy networks regularly expand the capacity of their network by building new network elements, known as the expansion planning problem.&#13;
A key constraint function in expansion planning problems is a nonlinear and nonconvex potential loss function. In order to improve the algorithmic performance of state-of-the-art MINLP solvers, this paper presents an algebraic description for the convex envelope of this function. Through a thorough computational study, we show that this tighter relaxation tremendously improve the performance of the MINLP solver SCIP on a large test set of practically relevant instances for the expansion planning problem. In particular, the results show that our achievements lead to an improvement of the solver performance for a development version by up to 58%.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-81459</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <author>Ralf Lenz</author>
    <submitter>Ralf Lenz</submitter>
    <author>Felipe Serrano</author>
    <series>
      <title>ZIB-Report</title>
      <number>21-05</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Convex envelopes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed-Integer Nonlinear Programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Expansion planning of energy networks</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="persons" number="lenz">Lenz, Ralf</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="Mathematical Algorithmic Intelligence">Mathematical Algorithmic Intelligence</collection>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8145/ZR_21-05.pdf</file>
  </doc>
  <doc>
    <id>1234</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2011-03-15</completedDate>
    <publishedDate>2011-03-15</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Gas Network Topology Optimization for Upcoming Market Requirements</title>
    <abstract language="eng">Gas distribution networks are complex structures that consist of&#13;
passive pipes, and active, controllable elements such as valves and&#13;
compressors. Controlling such network means to find a suitable setting&#13;
for all active components such that a nominated amount of gas can be&#13;
transmitted from entries to exits through the network, without&#13;
violating physical or operational constraints. The control of a&#13;
large-scale gas network is a challenging task from a practical point&#13;
of view. In most companies the actual controlling process is supported&#13;
by means of computer software that is able to simulate the flow of the&#13;
gas. However, the active settings have to be set manually within such&#13;
simulation software. The solution quality thus depends on the&#13;
experience of a human planner.&#13;
&#13;
When the gas network is insufficient for the transport then topology&#13;
extensions come into play. Here a set of new pipes or active elements&#13;
is determined such that the extended network admits a feasible control&#13;
again. The question again is how to select these extensions and where&#13;
to place them such that the total extension costs are&#13;
minimal. Industrial practice is again to use the same simulation&#13;
software, determine extensions by experience, add them to the virtual&#13;
network, and then try to find a feasible control of the active&#13;
elements. The validity of this approach now depends even more on the&#13;
human planner.&#13;
&#13;
Another weakness of this manual simulation-based approach is that it&#13;
cannot establish infeasibility of a certain gas nomination, unless all&#13;
settings of the active elements are tried. Moreover, it is impossible&#13;
to find a cost-optimal network extension in this way.&#13;
In order to overcome these shortcomings of the manual planning&#13;
approach we present a new approach, rigorously based on mathematical&#13;
optimization. Hereto we describe a model for finding feasible&#13;
controls and then extend this model such that topology extensions can&#13;
additionally and simultaneously be covered. Numerical results for real-world instances are presented and&#13;
discussed.</abstract>
    <identifier type="serial">11-09</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-12348</identifier>
    <identifier type="doi">10.1109/EEM.2011.5953035</identifier>
    <enrichment key="SourceTitle">Appeared in: Engery Market (EEM), 2011 8th International Conference on the European, Zagreb, 25-27 May 2011, pp. 346-351</enrichment>
    <author>Armin Fügenschuh</author>
    <submitter>-empty- (Opus4 user: )</submitter>
    <author>Benjamin Hiller</author>
    <submitter>Jonas Schweiger</submitter>
    <author>Jesco Humpola</author>
    <author>Thorsten Koch</author>
    <author>Thomas Lehmann</author>
    <author>Robert Schwarz</author>
    <author>Jonas Schweiger</author>
    <author>Jácint Szabó</author>
    <series>
      <title>ZIB-Report</title>
      <number>11-09</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Mathematical Optimization</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Gas Distribution Networks</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Topology Planning</value>
    </subject>
    <collection role="msc" number="76N25">Flow control and optimization</collection>
    <collection role="msc" number="90B10">Network models, deterministic</collection>
    <collection role="msc" number="90C11">Mixed integer programming</collection>
    <collection role="msc" number="90C30">Nonlinear programming</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="fuegenschuh">Fügenschuh, Armin</collection>
    <collection role="persons" number="koch">Koch, Thorsten</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="ForNe">ForNe</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="schweiger">Schweiger, Jonas</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1234/ZR-11-09.pdf</file>
  </doc>
  <doc>
    <id>4311</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-11-21</completedDate>
    <publishedDate>2013-11-21</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Primal Heuristic for MINLP based on Dual Information</title>
    <abstract language="eng">We present a novel heuristic algorithm to identify feasible solutions of a mixed-integer nonlinear programming problem arising in natural gas transportation: the selection of new pipelines to enhance the network's capacity to a desired level in a cost-efficient way. We solve this problem in a linear programming based branch-and-cut approach, where we deal with the nonlinearities by linear outer approximation and spatial branching. At certain nodes of the branching tree, we compute a KKT point for a nonlinear relaxation. Based on the information from the KKT point we alter some of the integer variables in a locally promising way. We describe this heuristic for general MINLPs and then show how to tailor the heuristic to exploit our problem-specific structure. On a test set of real-world instances, we are able to increase the chance of identifying feasible solutions by some order of magnitude compared to standard MINLP heuristics that are already built in the general-purpose MINLP solver SCIP.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-43110</identifier>
    <identifier type="doi">10.1007/s13675-014-0029-0</identifier>
    <enrichment key="SourceTitle">Appeared under the title "A primal heuristic for optimizing the topology of gas networks based on dual information" in: EURO Journal on Computational Optimization 2014</enrichment>
    <author>Jesco Humpola</author>
    <submitter>Armin Fügenschuh</submitter>
    <author>Armin Fügenschuh</author>
    <author>Thomas Lehmann</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-49</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed-Integer Nonlinear Programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Relaxations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Heuristics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Duality</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Nonlinear Network Design Applications</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="fuegenschuh">Fügenschuh, Armin</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="ForNe">ForNe</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4311/ZR-13-49.pdf</file>
  </doc>
  <doc>
    <id>6109</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-11-23</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Analysis of operating modes of complex compressor stations</title>
    <abstract language="eng">We consider the modeling of operation modes for complex compressor stations (i.e., ones with several in- or outlets) in gas networks. In particular, we propose a refined model that allows to precompute tighter relaxations for each operation mode. These relaxations may be used to strengthen the compressor station submodels in gas network optimization problems. We provide a procedure to obtain the refined model from the input data for the original model.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-61092</identifier>
    <enrichment key="SourceTitle">Appeared in Proceedings of Operations Research 2016, Springer, 2017.</enrichment>
    <enrichment key="FulltextUrl">https://link.springer.com/chapter/10.1007/978-3-319-55702-1_34</enrichment>
    <author>Benjamin Hiller</author>
    <submitter>Tom Walther</submitter>
    <author>René Saitenmacher</author>
    <author>Tom Walther</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-61</number>
    </series>
    <collection role="msc" number="05-XX">COMBINATORICS (For finite fields, see 11Txx)</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="TRR154-A04">TRR154-A04</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6109/ZR-16-61.pdf</file>
  </doc>
  <doc>
    <id>6746</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-03-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Improving branching for disjunctive polyhedral models using approximate convex decompositions</title>
    <abstract language="eng">Disjunctive sets arise in a variety of optimization models and much esearch has been devoted to obtain strong relaxations for them. This paper focuses on the evaluation of the relaxation during the branch-and-bound search process. We argue that the branching possibilities (\ie binary variables) of the usual formulations are unsuitable to obtain strong bounds early in the search process as they do not capture the overall shape of the the entire disjunctive set. To analyze and exploit the shape of the disjunctive set we propose to compute a hierarchy of approximate convex decompositions and show how to extend the known formulations to obtain improved branching behavior.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-67462</identifier>
    <author>Benjamin Hiller</author>
    <submitter>Benjamin Hiller</submitter>
    <author>Tom Walther</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-68</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>approximate convex decomposition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>branch-and-bound</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>convex hull reformulation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>disjunctive set</value>
    </subject>
    <collection role="ccs" number="J.">Computer Applications</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="TRR154-A04">TRR154-A04</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6746/ZR-17-68.pdf</file>
  </doc>
  <doc>
    <id>6156</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-12-22</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimal Looping of Pipelines in Gas Networks</title>
    <abstract language="eng">In this paper, we compare several approaches for the problem of gas network expansions using loops, that is, to build new pipelines in parallel to existing ones. We present different model formulations for the problem of continuous loop expansions as well as discrete loop expansions. We then analyze problem properties, such as the structure and convexity of the underlying feasible regions. The paper concludes with a computational study comparing the continuous and the discrete formulations.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-61564</identifier>
    <author>Ralf Lenz</author>
    <submitter>Ralf Lenz</submitter>
    <author>Robert Schwarz</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-67</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed Integer Nonlinear Programming</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Gas Network Applications</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Expansion Planning</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="lenz">Lenz, Ralf</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6156/ZR-16-67.pdf</file>
  </doc>
  <doc>
    <id>6151</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-12-22</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Using Bilevel Optimization to find Severe Transport Situations in Gas Transmission Networks</title>
    <abstract language="eng">In the context of gas transmission in decoupled entry-exit systems, many approaches to determine the network capacity are based on the evaluation of realistic and severe transport situations. In this paper, we review the Reference Point Method, which is an algorithm used in practice to generate a set of scenarios using the so-called transport moment as a measure for severity. We introduce a new algorithm for finding severe transport situations that considers an actual routing of the flow through the network and is designed to handle issues arising from cyclic structures in a more dynamical manner. Further, in order to better approximate the physics of gas, an alternative, potential based flow formulation is proposed. The report concludes with a case study based on data from the benchmark library GasLib.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-61519</identifier>
    <author>Kai Hennig</author>
    <submitter>Kai Hennig</submitter>
    <author>Robert Schwarz</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-68</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>bilevel optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>gas networks</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>network flow</value>
    </subject>
    <collection role="msc" number="49-XX">CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="msc" number="91-XX">GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="hennig">Hoppmann, Kai</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6151/ZR-16-68.pdf</file>
  </doc>
  <doc>
    <id>1515</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2012-04-24</completedDate>
    <publishedDate>2012-04-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The set of solutions to nomination validation in passive gas   transportation networks with a generalized flow formula</title>
    <abstract language="eng">In this paper we give an analytical description on the structure of&#13;
  solutions to the gas nomination validation problem in gas&#13;
  transportation networks. These networks are assumed to contain no&#13;
  active devices, only certain hypothetical pipelines, where the flow&#13;
  of gas is modeled by a generalized version of the quadratic&#13;
  Weymouth's equation. The purpose of considering generalized flow&#13;
  formulas is to be able to adapt our results to various gas network&#13;
  optimization problems involving gas flow formulas beyond Weymouth's&#13;
  equation. Such formulas can appear in leaves of branch and bound&#13;
  trees, or they can stem from discretization and linearization&#13;
  carried out at active devices. We call a balanced supply-demand&#13;
  vector a nomination, and the passive nomination validation problem&#13;
  is to decide whether there exist pressures at the nodes generating a&#13;
  given nomination. We prove that in our setup the pressure square&#13;
  vectors generating a given nomination form a one-dimensional&#13;
  connected and continuous curve in the pressure square space, and&#13;
  this curve is a line for the classical Weymouth's equation.  We also&#13;
  present a visual approach for the easy comprehension of how this&#13;
  solution curve arises; we give a short investigation of the set of&#13;
  feasible nominations; and finally we give a proof that the&#13;
  nomination validation problem in gas networks with active devices is&#13;
  NP-complete.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-15151</identifier>
    <author>Jácint Szabó</author>
    <submitter>Benjamin Hiller</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>11-44</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>pressure drop equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>gas networks</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>generalized flow formula</value>
    </subject>
    <collection role="ccs" number="G.">Mathematics of Computing</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="ForNe">ForNe</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1515/ZR-11-44.pdf</file>
  </doc>
  <doc>
    <id>1512</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2012-04-19</completedDate>
    <publishedDate>2012-04-19</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Optimierung Technischer Kapazitäten in Gasnetzen</title>
    <abstract language="deu">Die mittel- und längerfristige Planung für den Gastransport hat sich durch&#13;
Änderungen in den regulatorischen Rahmenbedingungen stark verkompliziert.&#13;
Kernpunkt ist die Trennung von Gashandel und -transport. Dieser Artikel&#13;
diskutiert die hieraus resultierenden mathematischen Planungsprobleme,&#13;
welche als Validierung von Nominierungen und Buchungen, Bestimmung der&#13;
technischen Kapazität und Topologieplanung bezeichnet werden. Diese&#13;
mathematischen Optimierungsprobleme werden vorgestellt und Lösungsansätze&#13;
skizziert.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-15121</identifier>
    <author>Alexander Martin</author>
    <submitter>Benjamin Hiller</submitter>
    <author>Björn Geißler</author>
    <author>Christine Hayn</author>
    <author>Benjamin Hiller</author>
    <author>Jesco Humpola</author>
    <author>Thorsten Koch</author>
    <author>Thomas Lehmann</author>
    <author>Antonio Morsi</author>
    <author>Marc Pfetsch</author>
    <author>Lars Schewe</author>
    <author>Martin Schmidt</author>
    <author>Rüdiger Schultz</author>
    <author>Robert Schwarz</author>
    <author>Jonas Schweiger</author>
    <author>Marc Steinbach</author>
    <author>Bernhard Willert</author>
    <series>
      <title>ZIB-Report</title>
      <number>11-56</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Gasnetzplanung</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Technische Kapazitäten</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Nominierungsvalidierung</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Buchungsvalidierung</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Topologieplanung</value>
    </subject>
    <collection role="ccs" number="J.">Computer Applications</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="koch">Koch, Thorsten</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="ForNe">ForNe</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="schweiger">Schweiger, Jonas</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1512/ZR-11-56.pdf</file>
  </doc>
  <doc>
    <id>6743</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-03-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A System to Evaluate Gas Network Capacities: Concepts and Implementation</title>
    <abstract language="eng">In 2005 the European Union liberalized the gas market with a disruptive change and decoupled trading of natural gas from its transport. The gas is now transported by independent so-called transmissions system operators or TSOs. The market model established by the European Union views the gas transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer the maximum possible capacities at each entry and exit such that any resulting gas flow can be realized by the network. The revenue from selling these capacities more than one billion Euro in Germany alone, but overestimating the capacity might compromise the security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs.&#13;
&#13;
This is a report on a large project in mathematical optimization, set out to develop a new toolset for evaluating gas network capacities. The goals and the challenges as they occurred in the project are described, as well as the developments and design decisions taken to meet the requirements.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-67438</identifier>
    <note>An earlier version of this report is available as ZR 17-03 at&#13;
https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6193.</note>
    <author>Benjamin Hiller</author>
    <submitter>Jonas Schweiger</submitter>
    <author>Thorsten Koch</author>
    <author>Lars Schewe</author>
    <author>Robert Schwarz</author>
    <author>Jonas Schweiger</author>
    <series>
      <title>ZIB-Report</title>
      <number>18-11</number>
    </series>
    <collection role="msc" number="90B90">Case-oriented studies</collection>
    <collection role="msc" number="90C90">Applications of mathematical programming</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="koch">Koch, Thorsten</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="ForNe">ForNe</collection>
    <collection role="projects" number="TRR154-A04">TRR154-A04</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="schweiger">Schweiger, Jonas</collection>
    <collection role="institutes" number="enernet">Energy Network Optimization</collection>
    <collection role="persons" number="schwarz">Schwarz, Robert</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6743/ZR-18-11.pdf</file>
  </doc>
  <doc>
    <id>6627</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2017-12-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Gas Network Benchmark Models</title>
    <abstract language="eng">The simulation of gas transportation networks becomes increasingly more important as its use-cases broadens to more complex applications. Classically, the purpose of the gas network was the transportation of predominantly natural gas from a supplier to the consumer for long-term scheduled volumes. With the rise of renewable energy sources, gas-fired power plants are often chosen to compensate for the fluctuating nature of the renewables, due to their on-demand power generation capability. Such an only short-term plannable supply and demand setting requires sophisticated simulations of the gas network prior to the dispatch to ensure the supply of all customers for a range of possible scenarios and to prevent damages to the&#13;
gas network. In this work we describe the modelling of gas networks and present benchmark systems to test implementations and compare new or extended models.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-66274</identifier>
    <identifier type="doi">10.1007/11221_2018_5</identifier>
    <enrichment key="SourceTitle">published in Differential-Algebraic Equations Forum</enrichment>
    <author>Peter Benner</author>
    <submitter>Tom Streubel</submitter>
    <author>Sara Grundel</author>
    <author>Christian Himpe</author>
    <author>Christoph Huck</author>
    <author>Tom Streubel</author>
    <author>Caren Tischendorf</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-73</number>
    </series>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="enernet">Energy Network Optimization</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6627/gasbenchmark.pdf</file>
  </doc>
  <doc>
    <id>6463</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2017-07-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Integrating Lipschitzian Dynamical Systems using Piecewise Algorithmic Differentiation</title>
    <abstract language="eng">In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side \(F:R^n \to R^n\) based on a generalization of algorithmic differentiation. When applied to such a problem, the classical trapezoidal rule suffers from a loss of accuracy if the solution trajectory intersects a nondifferentiability of \(F\). The advantage of the proposed generalized trapezoidal rule is threefold: Firstly, we can achieve a higher convergence order than with the classical method. Moreover, the method is energy preserving for piecewise linear Hamiltonian systems. Finally, in analogy to the classical case we derive a third order interpolation polynomial for the numerical trajectory. In the smooth case the generalized rule reduces to the classical one. Hence, it is a proper extension of the classical theory. An error estimator is given and numerical results are presented.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-64639</identifier>
    <identifier type="doi">10.1080/10556788.2017.1378653</identifier>
    <enrichment key="SourceTitle">published at Optimization Methods and Software</enrichment>
    <author>Andreas Griewank</author>
    <submitter>Tom Streubel</submitter>
    <author>Richard Hasenfelder</author>
    <author>Manuel Radons</author>
    <author>Lutz Lehmann</author>
    <author>Tom Streubel</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-44</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Automatic Differentiation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Lipschitz Continuity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Piecewise Linearization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Nonsmooth</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Trapezoidal Rule</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Energy Preservation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Dense Output</value>
    </subject>
    <collection role="msc" number="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="enernet">Energy Network Optimization</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6463/ODE_paper_ZibReport.pdf</file>
  </doc>
  <doc>
    <id>6457</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2017-07-17</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Benefits and Limitations of Simplified Transient Gas Flow Formulations</title>
    <abstract language="eng">Although intensively studied in recent years, the optimization of the transient (time-dependent) control of large real-world gas networks is still out of reach for current state-of-the-art approaches.&#13;
For this reason, we present further simplifications of the commonly used model, which lead to a linear description of the gas flow on pipelines.&#13;
In an empirical analysis of real-world data, we investigate the properties of the involved quantities and evaluate the errors made by our simplification.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-64570</identifier>
    <identifier type="doi">10.1007/978-3-319-89920-6_32</identifier>
    <enrichment key="PeerReviewed">No</enrichment>
    <submitter>Felix Hennings</submitter>
    <author>Felix Hennings</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-39</number>
    </series>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="enernet">Energy Network Optimization</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6457/ZR-17-39.pdf</file>
  </doc>
  <doc>
    <id>6458</id>
    <completedYear/>
    <publishedYear>2017</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2017-07-17</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Generic Construction and Efficient Evaluation of Network DAEs and Their  Derivatives in the Context of Gas Networks</title>
    <abstract language="eng">We present a concept that provides an efficient description of differential-algebraic equations (DAEs) describing flow networks which provides the DAE function f and their Jacobians in an automatized way such that the sparsity pattern of the Jacobians is determined before their evaluation and previously determined values of f can be exploited. The user only has to provide the network topology and local function descriptions for each network element. The approach uses automatic differentiation (AD) and is adapted to switching element functions via the abs-normal-form (ANF).</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-64582</identifier>
    <identifier type="doi">10.1007/978-3-319-89920-6_83</identifier>
    <enrichment key="SourceTitle">published at Operations Research Proceedings 2017</enrichment>
    <author>Tom Streubel</author>
    <submitter>Tom Streubel</submitter>
    <author>Christian Strohm</author>
    <author>Philipp Trunschke</author>
    <author>Caren Tischendorf</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-41</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>compressed sparse row format</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>algorithmic differentiation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>abs-normal form</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>piecewise linear tangent approximation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>piecewise smooth</value>
    </subject>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="enernet">Energy Network Optimization</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6458/main.pdf</file>
  </doc>
  <doc>
    <id>5348</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Sufficient Pruning Conditions for MINLP in Gas Network Design</title>
    <abstract language="eng">One quarter of Europe’s energy demand is provided by natural gas distributed through a vast pipeline network covering the whole of Europe. At a cost of 1 million Euros per kilometer the extension of the European pipeline network is already a multi billion Euro business. Therefore, automatic planning tools that support the decision process are desired. We model the topology extension problem in gas networks by a mixed-integer nonlinear program (MINLP). This gives rise to a so-called active transmission problem, a continuous nonlinear non-convex feasibility problem which emerges from the MINLP model by ﬁxing all integral variables. In this article we offer novel sufficient conditions for proving the infeasibility of this active transmission problem. These conditions can be expressed in the form of a mixed-integer program (MILP), i.e., the infeasibility of a non-convex NLP can be certiﬁed by solving an MILP. These results provide an efficient bounding procedure in a branch-and-bound algorithm. Our computational results demonstrate a substantial speed-up for the necessary computations.</abstract>
    <identifier type="urn">urn:nbn:de:0297-zib-53489</identifier>
    <identifier type="doi">10.1007/s13675-016-0077-8</identifier>
    <enrichment key="SourceTitle">Appeared in: EURO Journal on Computational Optimization</enrichment>
    <author>Jesco Humpola</author>
    <submitter>Jesco Humpola</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>15-04</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Network Design</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Mixed-Integer Nonlinear Programming</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Infeasibility Detection</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="ForNe">ForNe</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5348/ZR-15-04.pdf</file>
  </doc>
  <doc>
    <id>1885</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-07-01</completedDate>
    <publishedDate>2013-07-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Unified View on Relaxations for a Nonlinear Network Flow Problem</title>
    <abstract language="eng">We consider a nonlinear nonconvex network flow problem that arises, for example, in natural gas or water transmission networks. Given is such network with active and passive components, that is, valves, compressors, pressure regulators (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes of the network. Besides flow conservation constraints in the nodes the flow must fulfill nonlinear nonconvex pressure loss constraints on the arcs subject to potential values (i.e., pressure levels) in both end nodes of each arc. The problem is how to numerically compute this flow and pressures. We review an existing approach of Maugis (1977) and extend it to the case of networks with active elements (for example, compressors). We further examine different ways of relaxations for the nonlinear network flow model. We compare different approaches based on nonlinear optimization numerically on a set of test instances.</abstract>
    <identifier type="urn">urn:nbn:de:0297-zib-18857</identifier>
    <author>Armin Fügenschuh</author>
    <submitter>Armin Fügenschuh</submitter>
    <author>Jesco Humpola</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-31</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Nonlinear Network Flow</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed-Integer Nonlinear Programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Relaxations</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="fuegenschuh">Fügenschuh, Armin</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="ForNe">ForNe</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1885/ZR-13-31.pdf</file>
  </doc>
  <doc>
    <id>1777</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-02-16</completedDate>
    <publishedDate>2013-02-16</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A New Class of Valid Inequalities for Nonlinear Network Design Problems</title>
    <abstract language="eng">We consider a nonlinear nonconvex network design problem that arises in the extension of natural gas transmission networks. Given is such network with active and passive components, that is, valves, compressors, pressure regulators (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes of the network. Besides flow conservation constraints in the nodes the flow must fulfill nonlinear nonconvex pressure loss constraints on the arcs subject to potential values (i.e., pressure levels) in both end nodes of each arc. Assume that there does not exist a feasible flow that fulfills all physical constraints and meets the desired entry and exit amounts. Then a natural question is where to extend the network by adding pipes in the most economic way such that this flow becomes feasible. Answering this question is computationally demanding because of the difficult problem structure. We use mixed-integer nonlinear programming techniques that rely on an outer approximation of the overall problem, and a branching on decision variables. We formulate a new class of valid inequalities (or cutting planes) which reduce the overall solution time when added to the formulation. We demonstrate the computational merits of our approach on test instances.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-17771</identifier>
    <identifier type="doi">10.1007/s00291-015-0390-2</identifier>
    <enrichment key="SourceTitle">Appeared in: OR Spectrum 2015</enrichment>
    <author>Jesco Humpola</author>
    <submitter>Armin Fügenschuh</submitter>
    <author>Armin Fügenschuh</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-06</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Network Design</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed-Integer Nonlinear Programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Cutting Planes</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="fuegenschuh">Fügenschuh, Armin</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="ForNe">ForNe</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1777/FuegenschuhHumpola2012__dual_var_cuts.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1777/ZR-13-06revisedversion.pdf</file>
  </doc>
  <doc>
    <id>1782</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-03-07</completedDate>
    <publishedDate>2013-03-07</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Mathematical Optimization for Challenging Network Planning Problems in Unbundled Liberalized Gas Markets</title>
    <abstract language="eng">The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. &#13;
While previously network operator and gas vendor where united, they were forced to split up into independent companies. &#13;
The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. &#13;
We show that these new paradigms lead to new and challenging mathematical optimization problems. &#13;
In order to solve them and to provide meaningful results for practice, all aspects of the underlying problems, such as combinatorics, stochasticity, uncertainty, and nonlinearity, have to be addressed. &#13;
With such special-tailored solvers, free network capacities and topological network extensions can, for instance, be determined.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-17821</identifier>
    <identifier type="doi">10.1007/s12667-013-0099-8</identifier>
    <enrichment key="SourceTitle">Appeared in:  Energy Systems  5 (2014) 449-473</enrichment>
    <author>Armin Fügenschuh</author>
    <submitter>Jonas Schweiger</submitter>
    <author>Björn Geißler</author>
    <author>Ralf Gollmer</author>
    <author>Christine Hayn</author>
    <author>Rene Henrion</author>
    <author>Benjamin Hiller</author>
    <author>Jesco Humpola</author>
    <author>Thorsten Koch</author>
    <author>Thomas Lehmann</author>
    <author>Alexander Martin</author>
    <author>Radoslava Mirkov</author>
    <author>Antonio Morsi</author>
    <author>Werner Römisch</author>
    <author>Jessica Rövekamp</author>
    <author>Lars Schewe</author>
    <author>Martin Schmidt</author>
    <author>Rüdiger Schultz</author>
    <author>Robert Schwarz</author>
    <author>Jonas Schweiger</author>
    <author>Claudia Stangl</author>
    <author>Marc Steinbach</author>
    <author>Bernhard Willert</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-13</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Gas Market Liberalization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Entry-Exit Model</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Gas Network Access Regulation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed-Integer Nonlinear Nonconvex Stochastic Optimization</value>
    </subject>
    <collection role="pacs" number="89.30.-g">Energy resources (see also 84.60.-h Direct energy conversion and storage)</collection>
    <collection role="msc" number="90B10">Network models, deterministic</collection>
    <collection role="msc" number="90C11">Mixed integer programming</collection>
    <collection role="msc" number="90C30">Nonlinear programming</collection>
    <collection role="msc" number="90C90">Applications of mathematical programming</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="fuegenschuh">Fügenschuh, Armin</collection>
    <collection role="persons" number="koch">Koch, Thorsten</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="ForNe">ForNe</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="schweiger">Schweiger, Jonas</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1782/ZR-13-13.pdf</file>
  </doc>
  <doc>
    <id>1653</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2012-11-19</completedDate>
    <publishedDate>2012-11-19</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions</title>
    <abstract language="eng">In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints.&#13;
We describe a two-stage approach to solve the resulting complex and numerically difficult mixed-integer non-convex nonlinear feasibility problem. The first phase consists of four distinct algorithms facilitating mixed-integer linear, mixed-integer nonlinear, reduced nonlinear, and complementarity constrained methods to compute possible settings for the discrete decisions. The second phase employs a precise continuous nonlinear programming model of the gas network. Using this setup, we are able to compute high quality solutions to real-world industrial instances whose size is significantly larger than networks that have appeared  in the literature previously.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-16531</identifier>
    <identifier type="doi">10.1080/10556788.2014.888426</identifier>
    <enrichment key="SourceTitle">Appeared in: Optimization Methods and Software 30 (2015) pp. 15-53</enrichment>
    <author>Marc Pfetsch</author>
    <submitter>Jonas Schweiger</submitter>
    <author>Armin Fügenschuh</author>
    <author>Björn Geißler</author>
    <author>Nina Geißler</author>
    <author>Ralf Gollmer</author>
    <author>Benjamin Hiller</author>
    <author>Jesco Humpola</author>
    <author>Thorsten Koch</author>
    <author>Thomas Lehmann</author>
    <author>Alexander Martin</author>
    <author>Antonio Morsi</author>
    <author>Jessica Rövekamp</author>
    <author>Lars Schewe</author>
    <author>Martin Schmidt</author>
    <author>Rüdiger Schultz</author>
    <author>Robert Schwarz</author>
    <author>Jonas Schweiger</author>
    <author>Claudia Stangl</author>
    <author>Marc Steinbach</author>
    <author>Stefan Vigerske</author>
    <author>Bernhard Willert</author>
    <series>
      <title>ZIB-Report</title>
      <number>12-41</number>
    </series>
    <collection role="ccs" number="D.">Software</collection>
    <collection role="ccs" number="J.">Computer Applications</collection>
    <collection role="msc" number="90-08">Computational methods</collection>
    <collection role="msc" number="90C11">Mixed integer programming</collection>
    <collection role="msc" number="90C30">Nonlinear programming</collection>
    <collection role="msc" number="90C90">Applications of mathematical programming</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="fuegenschuh">Fügenschuh, Armin</collection>
    <collection role="persons" number="koch">Koch, Thorsten</collection>
    <collection role="persons" number="vigerske">Vigerske, Stefan</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="ForNe">ForNe</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="schweiger">Schweiger, Jonas</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1653/ZR-12-41.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1653/ZR-12-41_revised.pdf</file>
  </doc>
  <doc>
    <id>6134</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-01-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">PySCIPOpt: Mathematical Programming in Python with the SCIP Optimization Suite</title>
    <abstract language="eng">SCIP is a solver for a wide variety of mathematical optimization problems. It is written in C and extendable due to its plug-in based design. However, dealing with all C specifics when extending SCIP can be detrimental to development and testing of new ideas. This paper attempts to provide a remedy by introducing PySCIPOpt, a Python interface to SCIP that enables users to write new SCIP code entirely in Python. We demonstrate how to intuitively model mixed-integer linear and quadratic optimization problems and moreover provide examples on how new Python plug-ins can be added to SCIP.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-61348</identifier>
    <identifier type="doi">10.1007/978-3-319-42432-3_37</identifier>
    <enrichment key="SourceTitle">Appeared in: Mathematical Software – ICMS 2016, Volume 9725, Pages 301-307</enrichment>
    <author>Stephen J. Maher</author>
    <submitter>Matthias Miltenberger</submitter>
    <author>Matthias Miltenberger</author>
    <author>João Pedro Pedroso</author>
    <author>Daniel Rehfeldt</author>
    <author>Robert Schwarz</author>
    <author>Felipe Serrano</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-64</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>SCIP, Mathematical optimization, Python, Modeling</value>
    </subject>
    <collection role="ccs" number="J.">Computer Applications</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="mip">Mathematical Optimization Methods</collection>
    <collection role="persons" number="miltenberger">Miltenberger, Matthias</collection>
    <collection role="persons" number="rehfeldt">Rehfeldt, Daniel</collection>
    <collection role="projects" number="ASTfSCM">ASTfSCM</collection>
    <collection role="projects" number="MIP-ZIBOPT">MIP-ZIBOPT</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6134/PySCIPOpt.pdf</file>
  </doc>
  <doc>
    <id>6017</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-08-16</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">SCIP-Jack – A solver for STP and variants with parallelization extensions</title>
    <abstract language="eng">The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. While often a strong relationship between different&#13;
Steiner tree problem variants can be observed, solution approaches employed so far have been&#13;
prevalently problem-specific. In contrast, this paper introduces a general-purpose solver that&#13;
can be used to solve both the classical Steiner tree problem and many of its variants without&#13;
modification. This versatility is achieved by transforming various problem variants into a&#13;
general form and solving them by using a state-of-the-art MIP-framework. The result is&#13;
a high-performance solver that can be employed in massively parallel environments and is&#13;
capable of solving previously unsolved instances.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-60170</identifier>
    <identifier type="doi">10.1007/s12532-016-0114-x</identifier>
    <enrichment key="SourceTitle">Mathematical Programming Computation, Vol. 9 (2)</enrichment>
    <author>Gerald Gamrath</author>
    <submitter>Daniel Rehfeldt</submitter>
    <author>Thorsten Koch</author>
    <author>Stephen J. Maher</author>
    <author>Daniel Rehfeldt</author>
    <author>Yuji Shinano</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-41</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Steiner tree problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>SCIP-Jack</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Steiner tree variants</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>maximum-weight connected subgraph</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>prize-collecting Steiner tree</value>
    </subject>
    <collection role="ccs" number="D.">Software</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="mip">Mathematical Optimization Methods</collection>
    <collection role="persons" number="gamrath">Gamrath, Gerald</collection>
    <collection role="persons" number="koch">Koch, Thorsten</collection>
    <collection role="persons" number="rehfeldt">Rehfeldt, Daniel</collection>
    <collection role="persons" number="shinano">Shinano, Yuji</collection>
    <collection role="projects" number="MIP-ZIBOPT">MIP-ZIBOPT</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6017/scipjack_ZIBreport.pdf</file>
  </doc>
  <doc>
    <id>6586</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2017-11-16</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Polyhedral 3D Models for compressors in gas networks</title>
    <abstract language="eng">Compressor machines are crucial elements in a gas transmission network, required to compensate for the pressure loss caused by friction in the pipes. Modelling all physical and technical details of a compressor machine involves a large amount of nonlinearity, which makes it hard to use such models in the optimization of large-scale gas networks. In this paper, we are going to describe a modelling approach for the operating range of a compressor machine, starting from a physical reference model and resulting in a polyhedral representation in the 3D space of mass flow throughput as well as in- and outlet pressure.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-65864</identifier>
    <author>Tom Walther</author>
    <submitter>Benjamin Hiller</submitter>
    <author>Benjamin Hiller</author>
    <author>René Saitenmacher</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-66</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>gas compressor modeling, polyhedral model, accuracy, z factor</value>
    </subject>
    <collection role="ccs" number="J.">Computer Applications</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="TRR154-A04">TRR154-A04</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6586/ZR-17-66.pdf</file>
  </doc>
  <doc>
    <id>6744</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-03-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Modelling compressor stations in gas networks</title>
    <abstract language="eng">Gas networks are an important application area for optimization. When considering long-range transmission, compressor stations play a crucial role in these applications. The purpose of this report is to collect and systematize the models used for compressor stations in the literature. The emphasis is on recent work on simple yet accurate polyhedral models that may replace more simplified traditional models without increasing model complexity. The report also describes an extension of the compressor station data available in GasLib (http://gaslib.zib.de/) with the parameters of these models.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-67443</identifier>
    <author>Benjamin Hiller</author>
    <submitter>Benjamin Hiller</submitter>
    <author>Tom Walther</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-67</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>MINLP model</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>compressor station</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>gas compressor modeling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonlinear model</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polyhedral model</value>
    </subject>
    <collection role="ccs" number="J.">Computer Applications</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="TRR154-A04">TRR154-A04</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6744/ZR-17-67.pdf</file>
  </doc>
  <doc>
    <id>6193</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2017-02-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A System to Evaluate Gas Network Capacities: Concepts and Implementation</title>
    <abstract language="eng">Since 2005, the gas market in the European Union is liberalized and the trading of natural gas is decoupled from its transport. The transport is done by so-called transmissions system    operators or TSOs. The market model established by the European Union views the gas   transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer maximum independent capacities at each entry and exit such that the resulting gas flows can be realized by the network without compromising security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs.&#13;
&#13;
This paper gives an overview of the toolset for evaluating gas network capacities that has been developed within the ForNe project, a joint research project of seven research partners initiated by Open Grid Europe, Germany's biggest TSO. While most of the relevant mathematics is described in the book "Evaluating Gas Network Capacities", this article sketches the system as a whole, describes some developments that have taken place recently, and gives some details about the current implementation.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-61931</identifier>
    <note>A revised and extended version is available as ZIB-Report 18-11.</note>
    <author>Benjamin Hiller</author>
    <submitter>Benjamin Hiller</submitter>
    <author>Thorsten Koch</author>
    <author>Lars Schewe</author>
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      <value>freely allocable   capacity</value>
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      <value>large-scale mixed-integer nonlinear programming</value>
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    <publishedYear>2016</publishedYear>
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    <language>eng</language>
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    <title language="eng">Piecewise linear secant approximation via Algorithmic Piecewise Differentiation</title>
    <abstract language="eng">It is shown how piecewise differentiable functions \(F: R^n → R^m\) that are defined by evaluation programs can be approximated locally by a piecewise linear model based on a pair of sample points x̌ and x̂. We show that the discrepancy between function and model at any point x is of the bilinear order O(||x − x̌|| ||x − x̂||). This is a little surprising since x ∈ R^n may vary over the whole Euclidean space, and we utilize only two function samples F̌ = F(x̌) and F̂ = F(x̂), as well as the intermediates computed during their evaluation. As an application of the piecewise linearization procedure we devise a generalized Newton’s method based on successive piecewise linearization and prove for it sufficient conditions for convergence and convergence rates equaling those of semismooth Newton. We conclude with the derivation of formulas for the numerically stable implementation of the aforedeveloped piecewise linearization methods.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-61642</identifier>
    <identifier type="doi">10.1080/10556788.2017.1387256</identifier>
    <enrichment key="SourceTitle">published at Optimization Methods and Software</enrichment>
    <author>Andreas Griewank</author>
    <submitter>Tom Streubel</submitter>
    <author>Tom Streubel</author>
    <author>Lutz Lehmann</author>
    <author>Richard Hasenfelder</author>
    <author>Manuel Radons</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-54</number>
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    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Automatic differentiation</value>
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    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Computational graph</value>
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      <type>uncontrolled</type>
      <value>Lipschitz continuity</value>
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    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Generalized Hermite interpolation</value>
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      <type>uncontrolled</type>
      <value>ADOL-C</value>
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    <collection role="msc" number="68-XX">COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)</collection>
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