First order optimality conditions for mathematical programs with semidefinite cone complementarity constraints
Abstract: In this paper we consider a mathematical program with semidefinite cone complementarity constraints (SDCMPCC). Such a problem is a matrix analogue of the mathematical program with (vector) complementarity constraints (MPCC) and includes MPCC as a special case. We derive explicit expressions for the strong-, Mordukhovich- and Clarke- (S-, M- and C-)stationary conditions and give constraint qualifications under which a local solution of SDCMPCC is a S-, M- and C-stationary point.
Keywords: mathematical program with semidefinite cone complementarity constraints, necessary optimality conditions, constraint qualifications, S-stationary conditions, M-stationary conditions, C-stationary conditions
Category 1: Complementarity and Variational Inequalities
Category 2: Convex and Nonsmooth Optimization
Category 3: Linear, Cone and Semidefinite Programming
Citation: Technical Report, November 15, 2010.
Entry Submitted: 11/16/2010
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