An Optimization Method for Semilinear Parabolic Relaxed Constrained Optimal Control Problems

Abstract

This paper addresses optimal control problems governed by semilinear parabolic partialdifferential equations, subject to control constraints and state constraints of integral type.Since such problems may not have classical solutions, a relaxed optimal control problem isconsidered. The relaxed control problem is discretized by using a finite element methodand the behavior in the limit of discrete optimality, admissibility and extremality propertiesis studied. A conditional descent method with penalties applied to the discrete problems isproposed. It is shown that the accumulation points of sequences produced by this methodare admissible and extremal for the discrete problem. Finally, numerical examples aregiven.