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

TL;DR

This paper develops necessary optimality conditions for a class of mathematical programs with equilibrium constraints, using nonsmooth analysis and variational techniques, addressing a less-explored area in optimization theory.

Contribution

It introduces new optimality conditions for MPECs with strong solution concepts, employing penalization and nonsmooth analysis methods.

Findings

Established necessary optimality conditions for the class of problems.

Derived error bounds for equilibrium constraints using variational analysis.

Extended the theoretical framework for strong solution concepts in MPECs.

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.