Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 307, Issue 1, Pages 350-369Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2004.10.032
Keywords
mathematical program with equilibrium constraints; necessary optimality conditions; sufficient optimality conditions; constraint qualifications
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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. (c) 2004 Elsevier Inc. All rights reserved.
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