A Smoothing Method for a Mathematical Program with P-Matrix Linear Complementarity Constraints

Xiaojun Chen, Masao Fukushima

Research output: Journal article publicationJournal articleAcademic researchpeer-review

36 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)223-246
Number of pages24
JournalComputational Optimization and Applications
Issue number3
Publication statusPublished - 1 Mar 2004
Externally publishedYes


  • Mathematical program with equilibrium constraints
  • P-matrix linear complementarity problem
  • Reformulation
  • Smoothing approximation

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization
  • Management Science and Operations Research
  • Computational Mathematics


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