Complementarity Constraint Qualifications and Simplified B-Stationarity Conditions for Mathematical Programs with Equilibrium Constraints

Authors:
Jong-Shi Pang;Masao Fukushima
Affiliations:
Department of Mathematical Sciences, Whiting School of Engineering, The Johns Hopkins University, Baltimore, Maryland 21218-2682, USA. jsp@vicp1.mts.jhu.edu;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan. fuku@kuamp.kyoto-u.ac.jp
Venue:
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Year:
1999

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Abstract

With the aid of some novel complementarityconstraint qualifications, we derive some simplified primal-dualcharacterizations of a B-stationary point for a mathematical programwith complementarity constraints (MPEC). The approach is basedon a locally equivalent piecewise formulation of such a programnear a feasible point. The simplified results, which rely heavilyon a careful dissection and improved understanding of the tangentcone of the feasible region of the program, bypass thecombinatorial characterization that is intrinsic to B-stationarity.