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Numerical Mathematics and Optimization

TALK: Patrick Mehlitz (Technische Universität Bergakademie Freiberg) [English]

On optimal control problems with control complementarity constraints
Date: 04/18/2018, 5:00 PM
Location: Hubland Nord, Geb. 30, 30.02.003
Organizer: Lehrstuhl für Mathematik VII
Speaker: Patrick Mehlitz

Complementarity constraints on control functions can be used to model switching requirements or result from transferring a bilevel optimal control problem with lower level control constraints into a single-level optimization problem using lower level optimality conditions.

In this talk, several different features of optimal control problems with complementarity constraints are addressed. First, it will be demonstrated that the existence of optimal solutions is closely related to the underlying function space setting. Due to the complementarity structure, constraint qualifications of reasonable strength fail to hold at all feasible points of the optimal control problem. However, it will be shown that necessary optimality conditions of strong stationarity-type are valid at locally optimal solutions. Finally, a penalty method based on smoothed NCP-functions is presented which can be used to compute globally optimal solutions of optimal control problems with control complementarity constraints. Some convergence results are discussed as well.

This talk is based on joint ongoing work with Christian Clason.