Document Type

Technical Report

Abstract

The paper concerns a new class of optimization-related problems called Equilibrium Problems with Equilibrium Constraints (EPECs). One may treat them as two level hierarchical problems, which involve equilibria at both lower and upper levels. Such problems naturally appear in various applications providing an equilibrium counterpart (at the upper level) of Mathematical Programs with Equilibrium Constraints (MPECs). We develop a unified approach to both EPECs and MPECs from the viewpoint of multiobjective optimization subject to equilibrium constraints. The problems of this type are intrinsically nonsmooth and require the use of generalized differentiation for their analysis and applications. This paper presents necessary optimality conditions for EPECs in finite-dimensional spaces based an advanced generalized variational tools of variational analysis. The optimality conditions are derived in normal form under certain qualification requirements, which can be regarded as proper analogs of the classical Mangasarian-Fromovitz constraint qualification in the general settings under consideration.

Number in Series

2003.17

Disciplines

Applied Mathematics | Mathematics

Comments

Dedicated to Olvi Mangasarian on occasion of his 70th birthday. This research was partly supported by the National Science Foundation under grants DMS-0072179 and DMS-0304989.

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