(1) Department of Mathematical System Science, Faculty of Science and Technology, Hirosaki, 036-8561, Japan;(2) Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan
Abstract:
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. Preliminary numerical results indicate that the method and convex reformulation are promising.