Solving invex multitime control problems with first‐order PDE constraints via the absolute value exact penalty method

Abstract

SummaryIn this paper, a nonconvex multitime control problem with first‐order PDE constraints is considered. Then, we investigate the absolute value exact penalty function method which is used for solving the aforesaid control problem. Namely, in order to ensure the effective use of the absolute value exact penalty function method in the considered case, the most important property of any exact penalty function method, that is, exactness of the penalization, is analyzed in the case when the aforementioned method is applied for solving the considered multitime control problem with first‐order PDE constraints in which the functionals involved are nonconvex. Thus, the equivalence between an optimal solution of the aforementioned control problem and a minimizer of its associated unconstrained multitime control problem constructed in the used absolute value exact penalty function method is proved under appropriate invexity hypotheses.