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<export-example>
  <doc>
    <id>22948</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>29</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>articler</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2018-12-20</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimality Conditions for a Class of Inverse Optimal Control Problems With Partial Differential Equations</title>
    <abstract language="eng">We consider bilevel optimization problems which can be interpreted as inverse optimal control problems. The lower-level problem is an optimal control problem with a parametrized objective function. The upper-level problem is used to identify the parameters of the lower-level problem. Our main focus is the derivation of first-order necessary optimality conditions. We prove C-stationarity of local solutions of the inverse optimal control problem and give a counterexample to show that strong stationarity might be violated at a local minimizer.</abstract>
    <parentTitle language="eng">Optimization: A Journal of Mathematical Programming and Operations Research</parentTitle>
    <identifier type="doi">10.1080/02331934.2018.1495205</identifier>
    <identifier type="url">https://www.tandfonline.com/doi/full/10.1080/02331934.2018.1495205</identifier>
    <identifier type="issn">0233-1934</identifier>
    <identifier type="issn">1029-4945</identifier>
    <enrichment key="BTU">nicht an der BTU erstellt / not created at BTU</enrichment>
    <author>
      <firstName>Felix</firstName>
      <lastName>Harder</lastName>
    </author>
    <submitter>
      <firstName>Gerd</firstName>
      <lastName>Wachsmuth</lastName>
    </submitter>
    <author>
      <firstName>Gerd</firstName>
      <lastName>Wachsmuth</lastName>
    </author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Inverse optimal control problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimality condition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>C-stationarity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>strong stationarity</value>
    </subject>
    <collection role="institutes" number="1309">FG Optimale Steuerung</collection>
  </doc>
  <doc>
    <id>23110</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>312</pageFirst>
    <pageLast>338</pageLast>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>40</volume>
    <type>articler</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2019-01-14</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Comparison of Optimality Systems for the Optimal Control of the Obstacle Problem</title>
    <abstract language="eng">We consider stationarity systems for the optimal control of the obstacle problem. The focus is on the comparison of several different systems which are provided in the literature. We obtain some novel results concerning the relations between these stationarity concepts.</abstract>
    <parentTitle language="eng">GAMM-Mitteilung</parentTitle>
    <identifier type="doi">10.1002/gamm.201740004</identifier>
    <identifier type="issn">0936-7195</identifier>
    <identifier type="issn">1522-2608</identifier>
    <enrichment key="BTU">nicht an der BTU erstellt / not created at BTU</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <author>
      <firstName>Felix</firstName>
      <lastName>Harder</lastName>
    </author>
    <submitter>
      <firstName>Gerd</firstName>
      <lastName>Wachsmuth</lastName>
    </submitter>
    <author>
      <firstName>Gerd</firstName>
      <lastName>Wachsmuth</lastName>
    </author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>obstacle problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>complementarity constraints</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>weak stationarity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>M-stationarity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>strong stationarity</value>
    </subject>
    <collection role="institutes" number="1309">FG Optimale Steuerung</collection>
  </doc>
  <doc>
    <id>23200</id>
    <completedYear/>
    <publishedYear>2019</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>153</pageFirst>
    <pageLast>188</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>26</volume>
    <type>articler</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2019-01-18</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A guided tour of polyhedric sets: basic properties, new results on intersections and applications</title>
    <abstract language="eng">The aim of this contribution is twofold. On the one hand, we give some new results concerning polyhedric sets. In particular, we show that sets with pointwise lower and upper bound are polyhedric in many important function spaces. Moreover, we show that the intersection of such a set with finitely many hyperplanes and half-spaces is polyhedric. We also provide counterexamples demonstrating that the intersection of polyhedric sets may fail to be polyhedric. On the other hand, we gather all important results from the literature concerning polyhedric sets in order to give a complete picture of the current knowledge. In particular, we illustrate the applications of polyhedricity.</abstract>
    <parentTitle language="eng">Journal of Convex Analysis</parentTitle>
    <identifier type="issn">0944-6532</identifier>
    <enrichment key="BTU">an der BTU erstellt / created at BTU</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <author>
      <firstName>Gerd</firstName>
      <lastName>Wachsmuth</lastName>
    </author>
    <submitter>
      <firstName>Gerd</firstName>
      <lastName>Wachsmuth</lastName>
    </submitter>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Polyhedricity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polyhedric set</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>directional differentiability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>projection</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>vector lattice</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>strong stationarity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>second-order conditions</value>
    </subject>
    <collection role="institutes" number="1309">FG Optimale Steuerung</collection>
  </doc>
  <doc>
    <id>23946</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1914</pageFirst>
    <pageLast>1932</pageLast>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>24</volume>
    <type>articler</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2019-04-16</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Strong Stationarity for Optimal Control of the Obstacle Problem with Control Constraints</title>
    <abstract language="eng">We consider the distributed optimal control of the obstacle problem with control constraints. Since Mignot proved in 1976 the necessity of a system which is equivalent to strong stationarity, it has been an open problem whether such a system is still necessary in the presence of control constraints. Using moderate regularity of the optimal control and an assumption on the control bounds (which is implied by $u_a &lt; 0 \le u_b$ quasi-everywhere in $\Omega$ in the case of an upper obstacle $y \le \psi$), we can answer this question in the affirmative. We also present counterexamples showing that strong stationarity may not hold if $u_a &lt; 0$ or $0 \le u_b$ are violated.</abstract>
    <parentTitle language="eng">SIAM Journal on Optimization :(SIOPT)</parentTitle>
    <identifier type="doi">10.1137/130925827</identifier>
    <identifier type="issn">1052-6234</identifier>
    <identifier type="issn">1095-7189</identifier>
    <enrichment key="BTU">nicht an der BTU erstellt / not created at BTU</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <author>
      <firstName>Gerd</firstName>
      <lastName>Wachsmuth</lastName>
    </author>
    <submitter>
      <firstName>Helen</firstName>
      <lastName>Jacob</lastName>
    </submitter>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>obstacle problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>strong stationarity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>complementarity conditions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>control constraints</value>
    </subject>
    <collection role="institutes" number="1309">FG Optimale Steuerung</collection>
  </doc>
  <doc>
    <id>26715</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>41</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>articler</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-01-13</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On Second-Order Optimality Conditionsfor Optimal Control Problems Governedby the Obstacle Problem</title>
    <abstract language="eng">This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on the active set, we derive various conditions that guarantee the local/global optimality of first-order stationary points and/or the local/global quadratic growth of the reduced objective function. Our analysis extends and refines existing results from the literature and also covers those situations where the problem at hand involves additional box-constraints on the control. As a byproduct, our approach shows in particular that Tikhonov regularized optimal control problems for the obstacle problem can be reformulated as state-constrained optimal control problems for the Poisson equation and that problems involving a subharmonic obstacle and a convex objective function are uniquely solvable. The paper concludes with three counterexamples which illustrate that rather peculiar effects can occur in the analysis of second-order optimality conditions for optimal control problems governed by the obstacle problem and that necessary second-order conditions for such problems may be hard to derive.</abstract>
    <parentTitle language="eng">Optimization</parentTitle>
    <identifier type="issn">1029-4945</identifier>
    <identifier type="issn">0233-1934</identifier>
    <identifier type="doi">10.1080/02331934.2020.1778686</identifier>
    <enrichment key="BTU">an der BTU erstellt / created at BTU</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="Fprofil">1 Energiewende und Dekarbonisierung / Energy Transition and Decarbonisation</enrichment>
    <enrichment key="Fprofil">4 Künstliche Intelligenz und Sensorik / Artificial Intelligence and Sensor Technology</enrichment>
    <author>
      <firstName>Constantin</firstName>
      <lastName>Christof</lastName>
    </author>
    <submitter>
      <firstName>Helen</firstName>
      <lastName>Jacob</lastName>
    </submitter>
    <author>
      <firstName>Gerd</firstName>
      <lastName>Wachsmuth</lastName>
    </author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>obstacle problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>second-order condition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-smooth optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>strong stationarity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>global optimality</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>quadratic growth</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>control constraints</value>
    </subject>
    <collection role="institutes" number="1309">FG Optimale Steuerung</collection>
  </doc>
  <doc>
    <id>26732</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>15</pageNumber>
    <edition/>
    <issue>2</issue>
    <volume>59</volume>
    <type>articler</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-01-14</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Elliptic quasi-variational inequalities under a smallness assumption: uniqueness, differential stability and optimal control</title>
    <abstract language="eng">We consider a quasi-variational inequality governed by a moving set. We employ the assumption that the movement of the set has a small Lipschitz constant. Under this requirement, we show that the quasi-variational inequality has a unique solution which depends Lipschitz-continuously on the source term. If the data of the problem is (directionally) differentiable, the solution map is directionally differentiable as well. We also study the optimal control of the quasi-variational inequality and provide necessary optimality conditions of strongly stationary type.</abstract>
    <parentTitle language="eng">Calculus of Variations and Partial Differential Equations</parentTitle>
    <identifier type="issn">1432-0835</identifier>
    <identifier type="issn">0944-2669</identifier>
    <identifier type="doi">10.1007/s00526-020-01743-3</identifier>
    <enrichment key="BTU">an der BTU erstellt / created at BTU</enrichment>
    <enrichment key="Artikelnummer">82</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <enrichment key="Fprofil">1 Energiewende und Dekarbonisierung / Energy Transition and Decarbonisation</enrichment>
    <enrichment key="Fprofil">4 Künstliche Intelligenz und Sensorik / Artificial Intelligence and Sensor Technology</enrichment>
    <author>
      <firstName>Gerd</firstName>
      <lastName>Wachsmuth</lastName>
    </author>
    <submitter>
      <firstName>Helen</firstName>
      <lastName>Jacob</lastName>
    </submitter>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>quasi-variational inequality</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>uniqueness</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>directional differentiability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>strong stationarity</value>
    </subject>
    <collection role="institutes" number="1309">FG Optimale Steuerung</collection>
  </doc>
  <doc>
    <id>28064</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>35</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>articlenr</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-12-03</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">First-order conditions for the optimal control of the obstacle problem with state constraints</title>
    <abstract language="eng">We consider an optimal control problem in which the state is governed by an unilateral obstacle problem (with obstacle from below) and restricted by a pointwise state constraint (from above). In the presence of control constraints, we prove, via regularization of the state constraints, that a system of C-stationarity is necessary for optimality. In the absence of control constraints, we show that local minimizers are even strongly stationary by a careful discussion of the primal first-order conditions of B-stationary type.</abstract>
    <parentTitle language="eng">arXiv</parentTitle>
    <identifier type="url">https://arxiv.org/abs/2012.15324</identifier>
    <enrichment key="BTU">an der BTU erstellt / created at BTU</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="Fprofil">1 Energiewende und Dekarbonisierung / Energy Transition and Decarbonisation</enrichment>
    <enrichment key="Fprofil">4 Künstliche Intelligenz und Sensorik / Artificial Intelligence and Sensor Technology</enrichment>
    <author>
      <firstName>Ira</firstName>
      <lastName>Neitzel</lastName>
    </author>
    <submitter>
      <firstName>Helen</firstName>
      <lastName>Jacob</lastName>
    </submitter>
    <author>
      <firstName>Gerd</firstName>
      <lastName>Wachsmuth</lastName>
    </author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Obstacle problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>state constraints</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>C-stationarity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>strong stationarity</value>
    </subject>
    <collection role="institutes" number="1309">FG Optimale Steuerung</collection>
  </doc>
</export-example>
