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Notes on some constraint qualifications for mathematical programs with equilibrium constraints. (English) Zbl 1280.90115
From the introduction: “Mathematical program with equilibrium constraints (MPEC) plays an important role in many fields such as engineering design, economic equilibria, transportation science, multilevel game, and mathematical programming itself. However, this kind of problems is generally difficult to deal with because their constraints fail to satisfy the standard Mangasarian-Fromovitz constraint qualification at any feasible point.”
In this paper, the authors investigate the weakest constraint qualifications for Bouligand and Mordukhovich stationarities for MPEC and show that there is indeed a gap between Bouligand-stationarity and Mordukhovich-stationarity. They also show that the MPEC relaxed constant positive linear dependence condition can ensure any locally optimal solution to be Mordukhovich stationary. The relations among the existing MPEC constraint qualifications are given, too.

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