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<export-example>
  <doc>
    <id>335</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>683</pageFirst>
    <pageLast>709</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>292</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2020-10-06</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Solving joint chance constrained problems using regularization and Benders' decomposition</title>
    <abstract language="eng">In this paper we investigate stochastic programs with joint chance constraints. We consider discrete scenario set and reformulate the problem by adding auxiliary variables. Since the resulting problem has a difficult feasible set, we regularize it. To decrease the dependence on the scenario number, we propose a numerical method by iteratively solving a master problem while adding Benders cuts. We find the solution of the slave problem (generating the Benders cuts) in a closed form and propose a heuristic method to decrease the number of cuts. We perform a numerical study by increasing the number of scenarios and compare our solution with a solution obtained by solving the same problem with continuous distribution.</abstract>
    <parentTitle language="eng">Annals of Operations Research</parentTitle>
    <identifier type="doi">10.1007/s10479-018-3091-9</identifier>
    <enrichment key="SubmissionStatus">in press</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International</licence>
    <author>Lukas Adam</author>
    <author>Martin Branda</author>
    <author>Holger Heitsch</author>
    <author>René Henrion</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>chance constrained programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimality conditions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>regularization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Benders cuts</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>gas networks</value>
    </subject>
    <collection role="institutes" number="">Weierstraß-Institut für Angewandte Analysis und Stochastik</collection>
    <collection role="subprojects" number="">B04</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/335/ABHH18_Preprint.pdf</file>
  </doc>
  <doc>
    <id>296</id>
    <completedYear>2019</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2019-12-17</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An enumerative formula for the spherical cap discrepancy</title>
    <abstract language="eng">The spherical cap discrepancy is a widely used measure for how uniformly a sample of points on the sphere is distributed. Being hard to compute, this discrepancy measure is typically replaced by some lower or upper estimates when designing optimal sampling schemes for the uniform distribution on the sphere. In this paper, we provide a fully explicit, easy to implement enumerative formula for the spherical cap discrepancy. Not surprisingly, this formula is of combinatorial nature and, thus, its application is limited to spheres of small dimension and moderate sample sizes. Nonetheless, it may serve as a useful calibrating tool for testing the efficiency of sampling schemes and its explicit character might be useful also to establish necessary optimality conditions when minimizing the discrepancy with respect to a sample of given size.</abstract>
    <identifier type="doi">10.1016/j.cam.2021.113409</identifier>
    <enrichment key="SubmissionStatus">in press</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International</licence>
    <author>Holger Heitsch</author>
    <author>René Henrion</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>spherical cap discrepancy</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>uniform distribution on sphere</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimality conditions</value>
    </subject>
    <collection role="institutes" number="">Weierstraß-Institut für Angewandte Analysis und Stochastik</collection>
    <collection role="subprojects" number="">B04</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/296/CapDiscrepancy19.pdf</file>
  </doc>
  <doc>
    <id>142</id>
    <completedYear>2017</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2017-05-23</completedDate>
    <publishedDate>2017-07-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On M-stationarity conditions in MPECs and the associated qualification conditions</title>
    <abstract language="eng">Depending on whether a mathematical program with equilibrium constraints&#13;
(MPEC) is considered in its original or its enhanced (via KKT conditions) form, the assumed qualification&#13;
conditions as well as the derived necessary optimality conditions may differ significantly. In this paper, we&#13;
study this issue when imposing one of the weakest possible qualification conditions, namely the calmness of&#13;
the perturbation mapping associated with the respective generalized equations in both forms of the MPEC.&#13;
It is well known that the calmness property allows one to derive the so-called M-stationarity conditions. The&#13;
restrictiveness of assumptions and the strength of conclusions in the two forms of the MPEC is also strongly&#13;
related to the qualification conditions on the “lower level”. For instance, even under the Linear Independence&#13;
Constraint Qualification (LICQ) for a lower level feasible set described by C 1 functions, the calmness properties&#13;
of the original and the enhanced perturbation mapping are drastically different. When passing to C 1,1 data, this&#13;
difference still remains true under the weaker Mangasarian-Fromovitz Constraint Qualification, whereas under&#13;
LICQ both the calmness assumption and the derived optimality conditions are fully equivalent for the original&#13;
and the enhanced form of the MPEC. After clarifying these relations, we provide a compilation of practically&#13;
relevant consequences of our analysis in the derivation of necessary optimality conditions. The obtained results&#13;
are finally applied to MPECs with structured equilibria.</abstract>
    <parentTitle language="eng">Mathematical Programming</parentTitle>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <author>Lukas Adam</author>
    <author>Rene Henrion</author>
    <author>Jiri Outrata</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>equilibrium constraints</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimality conditions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>constraint qualification</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>calmness</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>perturbation mapping</value>
    </subject>
    <collection role="institutes" number="">Weierstraß-Institut für Angewandte Analysis und Stochastik</collection>
    <collection role="subprojects" number="">B02</collection>
    <collection role="subprojects" number="">B04</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/142/calmness.pdf</file>
  </doc>
</export-example>
