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Complementarity constraint qualifications and simplified \(B\)-stationary conditions for mathematical programs with equilibrium constraints. (English) Zbl 1040.90560
Summary: With the aid of some novel complementarity constraint qualifications, we derive some simplified primal-dual characterizations of a B-stationary point for a mathematical program with complementarity constraints (MPEC). The approach is based on a locally equivalent piecewise formulation of such a program near a feasible point. The simplified results, which rely heavily on a careful dissection and improved understanding of the tangent cone of the feasible region of the program, bypass the combinatorial characterization that is intrinsic to B-stationarity.

90C46 Optimality conditions and duality in mathematical programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
91A65 Hierarchical games (including Stackelberg games)
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