On solving methods for elliptic optimal control problems with equilibrium constraints

Abstract

As a special case of mathematical program problems with equilibrium constraints, elliptic optimal control problems with equilibrium constraints have been drawing in- creasingly more attention and study, and the methods of solving elliptic optimal control problems with equilibrium constraints have moved forward as the development of math- ematical sciences. The main purpose of this paper is to introduce the development of studying elliptic optimal control problems with equilibrium constraints, and to compare the advantage and disadvantage of penalty function methods, finite element methods, conjugate gradient methods and iteration approximation. Further, some remarks and prospects of research in the future are proposed for the iteration methods.