Invited Session Mon.1.H 2035

Monday, 10:30 - 12:00 h, Room: H 2035

Cluster 24: Variational analysis [...]

Nonsmooth phenomena in optimal control


Chair: Roland Herzog



Monday, 10:30 - 10:55 h, Room: H 2035, Talk 1

Christian Meyer
Boundary control of the obstacle problem


The talk deals with optimal control problems governed by the obstacle problem, where the control is given by Neumann data. Several stationarity concepts for the problem under consideration and additionally second-order sufficient conditions are presented.



Monday, 11:00 - 11:25 h, Room: H 2035, Talk 2

Matthias Gerdts
Globalized semi-smooth Newton methods in optimal control problems with DAEs


This paper addresses the numerical solution of optimal control problems subject to differential-algebraic equations and mixed control-state constraints by semi-smooth Newton methods. A particular focus is on globalization techniques for semi-smooth Newton methods and on regularization and smoothing techniques for the Fischer-Burmeister function. An open problem for the convergence analysis remains the construction of a smoothing operator for the Fischer-Burmeister function. Numerical experiments on various problems without smoothing operator however suggest that the methods work well in practice and a superlinear convergence rate and mesh independence can be observed numerically.



Monday, 11:30 - 11:55 h, Room: H 2035, Talk 3

Frank Schmidt
Properties of the optimal value function and application to worst-case robust optimal control problems

Coauthor: Roland Herzog


Sufficient conditions ensuring weak lower semi-continuity of the optimal value function are presented. To this end, refined inner semi-continuity properties of set-valued maps are introduced which meet the needs of the weak topology in Banach spaces. The results are applied to prove the existence of solutions in various worst-case robust optimal control problems governed by semilinear elliptic partial differential equations.


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