Nonconvex interval-valued multitime control problems with first-order PDE constraints via the minimax exact penalty method

Abstract

The growing use of optimization models to help decision-making has created a demand for such tools that allow solving more real models of processes related to human activity in which hypotheses are not verified in a way specific for classical optimization. And just interval-valued optimization problems were developed for formulating such real-world problems which are usually not well defined and they contain uncertain data. In this paper, an interval-valued multitime control problem with first-order PDE constraints is considered. Then, the minimax exact penalty function method is used for solving the aforesaid interval-valued extremum problem. The most important property of all exact penalty function methods, that is, exactness of the penalization, is generalized to the case when one of such methods is used for solving an interval-valued multitime control problem. Namely, under appropriate invexity hypotheses, it is examined in the case of the minimax exact penalty function method which is used for solving the aforesaid interval-valued multitime control problem with the first-order PDE constraints.