Abstract
In this paper we study optimal control problems of systems governed by nonlinear evolution equations. First using a convexity hypothesis and the Cesari-Rockafellar reduction technique, we establish the existence of optimal admissible pairs. Then we examine the relaxation of the original problem. We consider two relaxation methods. One based.on transition probabilities and the other on the Γ—regularization of the cost functional. This way we derive three different formulations of the relaxed problem which we compare. Next we study the changes in the value of the problem when we perturb its data and relate variational stability and relaxability. Finally we derive necessary conditions for optimality using a penalty function approach.
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