Necessary and Sufficient Optimality Conditions for Mathematical Programs with Equilibrium Constraints

Jane Ye (janeyemath.uvic.ca)

Abstract: In this paper we consider a mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with complementarity constraints. Various stationary conditions for MPECs exist in literature due to different reformulations. We give a simple proof to the M-stationary condition and show that it is sufficient or locally sufficient for optimality under some MPEC generalized convexity assumptions. Moreover we propose new constraint qualifications for M-stationary conditions to hold. These new constraint qualifications include piecewise MFCQ, piecewise Slater condition, MPEC weak reverse convex constraint qualification, MPEC Arrow-Hurwicz-Uzawa constraint qualification, MPEC Zangwill constraint qualification, MPEC Kuhn-Tucker constraint qualification and MPEC Abadie constraint qualification.

Keywords: mathematical program with equilibrium constraints, necessary optimality conditions, sufficient optimality conditions, constraint qualifications

Category 1: Nonlinear Optimization

Category 2: Convex and Nonsmooth Optimization

Category 3: Complementarity and Variational Inequalities

Citation: Department of Mathematics and Statistics, University of Victoria, Canada

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Entry Submitted: 06/04/2004
Entry Accepted: 06/04/2004
Entry Last Modified: 10/20/2004

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