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Constraint qualifications for mathematical programs with equilibrium constraints and their local preservation property. (English) Zbl 1315.90054
This paper gives a synopsis (rich in content and with a lot of hints to other existing papers of this domain) about known and new dependencies between constraint qualifications for programs with equilibrium constraints (vanishing product of nonnegative continuously differentiable functions), supplementing results of former papers of the authors in [J. Optim. Theory Appl. 158, No. 1, 11–32 (2013; Zbl 1272.90085)] and of L. Guo and G.-H. Lin [J. Optim. Theory Appl. 156, No. 3, 600–616 (2013; Zbl 1280.90115)] and of L. Guo et al. [J. Optim. Theory Appl. 158, No. 1, 33–64 (2013; Zbl 1272.90089)]. Also, new variants of constraint qualifications and new techniques of proof (induction) are introduced. As the main point of the paper the authors show that most of the considered constraint qualifications have the local preservation property $$(Q)$$, that means, $$(Q)$$ holds also for an open set of admissible points around a point $$x$$, whenever $$(Q)$$ is valid at $$x$$. Results of isolatedness of local minimizers are added.

##### MSC:
 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 90C30 Nonlinear programming 49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 90C46 Optimality conditions and duality in mathematical programming
MacMPEC
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