Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2001-008 (September 14, 2001)

A Smoothing Method for a Mathematical Program with P-Matrix Linear Complementarity Constraints
by Xiaojun Chen and Masao Fukushima

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We consider a mathematical program whose constraints involve a parametric P-matrix linear complementarity problem with the design (upper level) variables as parameters. Solutions of this complementarity problem define a piecewise linear function of the parameters. We study a smoothing function of this function for solving the mathematical program. We investigate the limiting behaviour of optimal solutions, KKT points and B-stationary points of the smoothing problem. We show that a class of mathematical programs with P-matrix linear complementarity constraints can be reformulated as a piecewise convex program and solved through a sequence of continuously differentiable convex programs.