Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints |
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Authors: | Jane J Ye |
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Institution: | Department of Mathematics and Statistics, University of Victoria, PO Box 3045 STN CSC, Victoria, BC, V8W 3P4 Canada |
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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 for global or local 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. |
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Keywords: | Mathematical program with equilibrium constraints Necessary optimality conditions Sufficient optimality conditions Constraint qualifications |
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