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  <doc>
    <id>624</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2000-12-20</completedDate>
    <publishedDate>2000-12-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Affine Invariant Convergence Analysis for Inexact Augmented Lagrangian-SQP Methods</title>
    <abstract language="eng">An affine invariant convergence analysis for inexact augmented Lagrangian-SQP methods is presented. The theory is used for the construction of an accuracy matching between iteration errors and truncation errors, which arise from the inexact linear system solves. The theoretical investigations are illustrated numerically by an optimal control problem for the Burgers equation.</abstract>
    <identifier type="serial">00-56</identifier>
    <identifier type="opus3-id">625</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-6243</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM J. Control Optim. 41 (2003) 875-899</enrichment>
    <author>Stefan Volkwein</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>00-56</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonlinear programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>multiplier methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>affine invariant norms</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Burgers' equation</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="49M15">Newton-type methods</collection>
    <collection role="msc" number="65N99">None of the above, but in this section</collection>
    <collection role="msc" number="90C55">Methods of successive quadratic programming type</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/624/ZR-00-56.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/624/ZR-00-56.pdf</file>
  </doc>
  <doc>
    <id>638</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2001-06-07</completedDate>
    <publishedDate>2001-06-07</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Central Path towards the Numerical Solution of Optimal Control Problems</title>
    <abstract language="eng">A new approach to the numerical solution of optimal control problems including control and state constraints is presented. Like hybrid methods, the approach aims at combining the advantages of direct and indirect methods. Unlike hybrid methods, however, our method is directly based on interior-point concepts in function space --- realized via an adaptive multilevel scheme applied to the complementarity formulation and numerical continuation along the central path. Existence of the central path and its continuation towards the solution point is analyzed in some theoretical detail. An adaptive stepsize control with respect to the duality gap parameter is worked out in the framework of affine invariant inexact Newton methods. Finally, the performance of a first version of our new type of algorithm is documented by the successful treatment of the well-known intricate windshear problem.</abstract>
    <identifier type="serial">01-12</identifier>
    <identifier type="opus3-id">639</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-6380</identifier>
    <enrichment key="SourceTitle">Appeared under the title " Inexact Central Path Following Algorithms for Optimal Control Problems" in: SIAM J. Contr. Opt. 46 (3) (2007) 792-815</enrichment>
    <author>Martin Weiser</author>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>01-12</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>interior point methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>affine invariance</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="49M15">Newton-type methods</collection>
    <collection role="msc" number="65K10">Optimization and variational techniques [See also 49Mxx, 93B40]</collection>
    <collection role="msc" number="90C48">Programming in abstract spaces</collection>
    <collection role="msc" number="90C51">Interior-point methods</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/638/ZR-01-12.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/638/ZR-01-12.pdf</file>
  </doc>
  <doc>
    <id>640</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2001-07-03</completedDate>
    <publishedDate>2001-07-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible</title>
    <abstract language="eng">By computed tomography data (CT), the individual geometry of the mandible is quite well reproduced, also the separation between cortical and trabecular bone. Using anatomical knowledge about the architecture and the functional potential of the masticatory muscles, realistic situations were approximated. The solution of the underlying partial differential equations describing linear elastic material behaviour is provided by an adaptive finite element method. Estimations of the discretization error, local grid refinement, and multilevel techniques guarantee the reliability and efficiency of the method.</abstract>
    <identifier type="serial">01-14</identifier>
    <identifier type="opus3-id">641</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-6403</identifier>
    <enrichment key="SourceTitle">Appeared in: Proc. of 9th Workshop on the Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields, Ulm, Germany, 2002, CD-ROM</enrichment>
    <author>Bodo Erdmann</author>
    <author>Cornelia Kober</author>
    <author>Jens Lang</author>
    <author>Robert Sader</author>
    <author>Hans-Florian Zeilhofer</author>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>01-14</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mandible</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>sensitivity analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite element method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adaptive grid refinement</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="74B10">Linear elasticity with initial stresses</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/640/ZR-01-14.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/640/ZR-01-14.pdf</file>
  </doc>
  <doc>
    <id>1041</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-11-27</completedDate>
    <publishedDate>2007-11-27</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Discretization of Interior Point Methods for State Constrained Elliptic Optimal Control Problems: Optimal Error Estimates and Parameter Adjustment</title>
    <abstract language="eng">An adjustment scheme for the relaxation parameter of interior point approaches to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced. The method is based on error estimates of an associated finite element discretization of the relaxed problems and optimally selects the relaxation parameter in dependence on the mesh size of discretization. The finite element analysis for the relaxed problems is carried out and a numerical example is presented which confirms our analytical findings.</abstract>
    <identifier type="serial">07-40</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1069</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10414</identifier>
    <enrichment key="SourceTitle">Also: Priority Program 1253, German Research Foundation (DFG), Preprint-Number SPP1253-08-03 (2007)</enrichment>
    <author>Michael Hinze</author>
    <submitter>unknown unknown</submitter>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>07-40</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Elliptic optimal control problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>error estimates</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>interior point method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>pointwise state constraints</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="49J20">Optimal control problems involving partial differential equations</collection>
    <collection role="msc" number="49K20">Problems involving partial differential equations</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1041/ZR_07_40.pdf</file>
  </doc>
  <doc>
    <id>1049</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-12-21</completedDate>
    <publishedDate>2007-12-21</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Pointwise Nonlinear Scaling for Reaction-Diffusion-Equations</title>
    <abstract language="eng">Parabolic reaction-diffusion systems may develop sharp moving reaction fronts which pose a challenge even for adaptive finite element methods. We propose a method to transform the equation into an equivalent form that usually exhibits solutions which are easier to discretize, giving higher accuracy for a given number of degrees of freedom. The transformation is realized as an efficiently computable pointwise nonlinear scaling that is optimized for prototypical planar travelling wave solutions of the underlying reaction-diffusion equation. The gain in either performance or accuracy is demonstrated on different numerical examples.</abstract>
    <identifier type="serial">07-45</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1078</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10493</identifier>
    <enrichment key="SourceTitle">Appeared in: Applied Numerical Mathematics 59 (2009), pp. 1858-1869. DOI information: 10.1016/j.apnum.2009.01.010</enrichment>
    <author>Martin Weiser</author>
    <submitter>unknown unknown</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>07-45</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reaction-diffusion equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>travelling waves</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonlinear scaling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>discretization error</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="65M50">Mesh generation and refinement</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="ZIB-Cardio">ZIB-Cardio</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1049/ZR_07_45.pdf</file>
  </doc>
  <doc>
    <id>1031</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-11-08</completedDate>
    <publishedDate>2007-11-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Inertia Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization</title>
    <abstract language="eng">Fast nonlinear programming methods following the all-at-once approach usually employ Newton's method for solving linearized Karush-Kuhn-Tucker (KKT) systems. In nonconvex problems, the Newton direction is only guaranteed to be a descent direction if the Hessian of the Lagrange function is positive definite on the nullspace of the active constraints, otherwise some modifications to Newton's method are necessary. This condition can be verified using the signs of the KKT's eigenvalues (inertia), which are usually available from direct solvers for the arising linear saddle point problems. Iterative solvers are mandatory for very large-scale problems, but in general do not provide the inertia. Here we present a preconditioner based on a multilevel incomplete $LBL^T$ factorization, from which an approximation of the inertia can be obtained. The suitability of the heuristics for application in optimization methods is verified on an interior point method applied to the CUTE and COPS test problems, on large-scale 3D PDE-constrained optimal control problems, as well as 3D PDE-constrained optimization in biomedical cancer hyperthermia treatment planning. The efficiency of the preconditioner is demonstrated on convex and nonconvex problems with $150^3$ state variables and $150^2$ control variables, both subject to bound constraints.</abstract>
    <identifier type="serial">07-32</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1060</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10314</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM J. Scientific Computing 31 (2008) 939-960</enrichment>
    <author>Olaf Schenk</author>
    <submitter>unknown unknown</submitter>
    <author>Andreas Wächter</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>07-32</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonconvex constrained optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>interior-point method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>inertia</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>multilevel incomplete factorization</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="49M15">Newton-type methods</collection>
    <collection role="msc" number="65F10">Iterative methods for linear systems [See also 65N22]</collection>
    <collection role="msc" number="65K10">Optimization and variational techniques [See also 49Mxx, 93B40]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1031/ZR_07_32.pdf</file>
  </doc>
  <doc>
    <id>1059</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-02-12</completedDate>
    <publishedDate>2008-02-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Extended Mathematical Framework for Barrier Methods in Function Space</title>
    <abstract language="eng">An extended mathematical framework for barrier methods for state constrained optimal control compared to [Schiela, ZIB-Report 07-07] is considered. This allows to apply the results derived there to more general classes of optimal control problems, in particular to boundary control and finite dimensional control.</abstract>
    <identifier type="serial">08-07</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1088</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10593</identifier>
    <enrichment key="SourceTitle">Appeared in: Domain Decomposition Methods in Science and Engineering XVIII Bercovier, M.; Gander, M.J.; Kornhuber, R.; Widlund, O. (Eds.) 2009. Lecture Notes in Computational Science and Engineering 70, pp 201-208</enrichment>
    <author>Anton Schiela</author>
    <submitter>unknown unknown</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>08-07</number>
    </series>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1059/ZR_08_07.pdf</file>
  </doc>
  <doc>
    <id>9130</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>2023-07-06</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization</title>
    <abstract language="eng">The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-91309</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Fabian Danecker</submitter>
    <author>Fabian Danecker</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>23-19</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>shortest path</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>flight planning</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>free flight</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>global optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Newton's method</value>
    </subject>
    <collection role="ccs" number="">Global optimization (NEW)</collection>
    <collection role="ccs" number="">Boundary value problems</collection>
    <collection role="ccs" number="">Graph algorithms</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="msc" number="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MathPlus-TrU-4">MathPlus-TrU-4</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/9130/ZIB-Report-23-19.pdf</file>
  </doc>
  <doc>
    <id>5960</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>2016-06-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Using sparse kernels to design computer experiments with tunable precision</title>
    <abstract language="eng">Statistical methods to design computer experiments usually rely on a Gaussian process (GP) surrogate model, and typically aim at selecting design points (combinations of algorithmic and model parameters) that minimize the average prediction variance, or maximize the prediction accuracy for the hyperparameters of the GP surrogate.&#13;
In many applications, experiments have a tunable precision, in the sense that one software parameter controls the tradeoff between accuracy and computing time (e.g., mesh size in FEM simulations or number of Monte-Carlo samples).&#13;
We formulate the problem of allocating a budget of computing time over a finite set of candidate points for the goals mentioned above. This is a continuous optimization problem, which is moreover convex whenever the tradeoff function accuracy vs. computing time is concave.&#13;
On the other hand, using non-concave weight functions can help to identify sparse designs. In addition, using sparse kernel approximations drastically reduce the cost per iteration of the multiplicative weights updates that can be used to solve this problem.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-59605</identifier>
    <enrichment key="SourceTitle">Appeared in: Ana Colubi, Angela Blanco and Cristian Gatu (eds.) 22nd Intern. Conf. on Computational Statistics - COMSTAT 2016, Oviedo, Spain, 23-26 August 2016, Proceedings ISBN 978-90-73592-36-0. Pp. 397-408</enrichment>
    <author>Guillaume Sagnol</author>
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    <author>Martin Weiser</author>
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      <title>ZIB-Report</title>
      <number>16-33</number>
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      <language>eng</language>
      <type>uncontrolled</type>
      <value>Optimal design of computer experiments</value>
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    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Sparse kernels</value>
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    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Gaussian Process</value>
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    <publishedDate>2020-12-20</publishedDate>
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    <title language="eng">A Discrete-Continuous Algorithm for Free Flight Planning</title>
    <abstract language="eng">We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach.</abstract>
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    <identifier type="doi">10.3390/a14010004</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-81343</identifier>
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    <enrichment key="AcceptedDate">2020-12-20</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Fabian Danecker</submitter>
    <author>Fabian Danecker</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>20-33</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>shortest path</value>
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    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>flight planning</value>
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    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>free flight</value>
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    <subject>
      <language>eng</language>
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      <value>discrete-continuous algorithm</value>
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    <subject>
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      <value>optimal control</value>
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    <subject>
      <language>eng</language>
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      <value>discrete optimization</value>
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