# zbMATH — the first resource for mathematics

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.

##### MSC:
 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)
Full Text: