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  <doc>
    <id>399</id>
    <completedYear>2021</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>20</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2021-07-13</completedDate>
    <publishedDate>2021-07-13</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Time-Domain Decomposition for Optimal Control Problems Governed by Semilinear Hyperbolic Systems with Mixed Two-Point Boundary Conditions</title>
    <abstract language="eng">In this article, we continue our work (Krug et al., 2021) on time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations in that we now consider mixed two-point boundary value problems and provide an in-depth well-posedness analysis. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems on metric graphs with cycles. We design an iterative method based on the optimality systems that can be interpreted as a decomposition method for the original optimal control problem into virtual control problems on smaller time domains.</abstract>
    <parentTitle language="eng">Control and Cybernetics</parentTitle>
    <enrichment key="SubmissionStatus">Accepted</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Richard Krug</author>
    <author>Günter Leugering</author>
    <author>Alexander Martin</author>
    <author>Martin Schmidt</author>
    <author>Dieter Weninger</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Time-domain decomposition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Semilinear hyperbolic systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Convergence</value>
    </subject>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="subprojects" number="">A05</collection>
    <collection role="subprojects" number="">B07</collection>
    <collection role="subprojects" number="">B08</collection>
    <collection role="institutes" number="">Universität Trier</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/399/time-domain-decomp_tp_bnd_cond_preprint.pdf</file>
  </doc>
  <doc>
    <id>380</id>
    <completedYear>2021</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>9</issue>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2021-03-05</completedDate>
    <publishedDate>2021-03-05</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Presolving Linear Bilevel Optimization Problems</title>
    <abstract language="eng">Linear bilevel optimization problems are known to be strongly NP-hard and the computational techniques to solve these problems are often motivated by techniques from single-level mixed-integer optimization. Thus, during the last years and decades many branch-and-bound methods, cutting planes, or heuristics have been proposed. On the other hand, there is almost no literature on presolving linear bilevel problems although presolve is a very important ingredient in state-of-the-art mixed-integer optimization solvers. In this paper, we carry over standard presolve techniques from single-level optimization to bilevel problems and show that this needs to be done with great caution since a naive application of well-known techniques does often not lead to correctly presolved bilevel models. Our numerical study shows that presolve can also be very beneficial for bilevel problems but also highlights that these methods have a more heterogeneous effect on the solution process compared to what is known from single-level optimization. As a side result, our numerical experiments reveal that there is an urgent need for better and more heterogeneous test instance libraries to further propel the field of computational bilevel optimization.</abstract>
    <parentTitle language="eng">EURO Journal on Computational Optimization</parentTitle>
    <identifier type="doi">10.1016/j.ejco.2021.100020</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Thomas Kleinert</author>
    <author>Julian Manns</author>
    <author>Martin Schmidt</author>
    <author>Dieter Weninger</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Linear Bilevel Optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Presolve</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Computational Analysis</value>
    </subject>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="subprojects" number="">A05</collection>
    <collection role="subprojects" number="">Z01</collection>
    <collection role="subprojects" number="">B08</collection>
    <collection role="institutes" number="">Universität Trier</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/380/bilevel_presolve_preprint.pdf</file>
  </doc>
  <doc>
    <id>476</id>
    <completedYear>2021</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
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    <type>preprint</type>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-11-12</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Computing optimality certificates for convex mixed-integer nonlinear problems</title>
    <abstract language="eng">Every optimization problem has a corresponding verification problem which verifies whether a given optimal solution is in fact optimal. In the literature there are a lot of such ways to verify optimality for a given solution, e.g., the branch-and-bound tree. To simplify this task, Baes et al. introduced optimality certificates for convex mixed-integer nonlinear programs and proved that these are bounded in the number of integer variables. We introduce an algorithm to compute the certificates and conduct computational experiments. Through the experiments we show that the optimality certificates can be surprisingly small.</abstract>
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    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Katrin Halbig</author>
    <author>Lukas Hümbs</author>
    <author>Florian Rösel</author>
    <author>Lars Schewe</author>
    <author>Dieter Weninger</author>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="subprojects" number="">A05</collection>
    <collection role="subprojects" number="">B07</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/476/optimality_certificates_preprint.pdf</file>
  </doc>
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