Optimal control problems with control complementarity constraints

TL;DR

This paper investigates a class of optimal control problems with complementarity constraints, establishing existence of solutions, deriving optimality conditions, proposing a penalty method, and demonstrating its effectiveness through computational experiments.

Contribution

It introduces a novel penalty approach using Fischer-Burmeister functions for control problems with complementarity constraints and analyzes its theoretical properties.

Findings

Existence of optimal solutions in Sobolev spaces.

Derivation of strong stationarity optimality conditions.

Successful numerical implementation with computational results.

Abstract

A special class of optimal control problems with complementarity constraints on the control functions is studied. It is shown that such problems possess optimal solutions whenever the underlying control space is a first-order Sobolev space. After deriving necessary optimality conditions of strong stationarity-type, a penalty method based on the Fischer-Burmeister function is suggested and its theoretical properties are analyzed. Finally, the numerical treatment of the problem is discussed and results of computational experiments are presented.