On some optimality conditions for a class of problems in mathematical programming with equilibrium constraints

Abstract

This paper considers mathematical programs, whose constraints are expressed by a parameterized vector equilibrium problem. The latter is a well recognized framework, which is able to cover multicriteria optimization, vector variational inequalities and complementarity problems. As the solutions to vector equilibrium problems are here intended in a strong sense, the consequent MPEC problems result in a class still little explored by the existing literature. Some necessary optimality conditions for such programs are established following a penalization approach. To derive and express these conditions, concepts and tools of nonsmooth analysis are employed. In treating equilibrium constraints, by techniques of variational analysis some error bounds are obtained, which may be of independent interest.