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On the Guignard constraint qualification for mathematical programs with equilibrium constraints. (English) Zbl 1147.90397
Summary: We recapitulate the well-known fact that most of the standard constraint qualifications are violated for mathematical programs with equilibrium constraints (MPECs). We go on to show that the Abadie constraint qualification is only satisfied in fairly restrictive circumstances. In order to avoid this problem, we fall back on the Guignard constraint qualification (GCQ). We examine its general properties and clarify the position it occupies in the context of MPECs. We show that strong stationarity is a necessary optimality condition under GCQ. Also, we present several sufficient conditions for GCQ, showing that it is usually satisfied for MPECs.

MSC:
90C30 Nonlinear programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C46 Optimality conditions and duality in mathematical programming
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