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

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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.

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Authors and Affiliations

  1. Department of Mathematical System Science, Faculty of Science and Technology, Hirosaki, 036-8561, Japan

    Xiaojun Chen

  2. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Masao Fukushima

Authors
  1. Xiaojun Chen
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  2. Masao Fukushima
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Chen, X., Fukushima, M. A Smoothing Method for a Mathematical Program with P-Matrix Linear Complementarity Constraints. Computational Optimization and Applications 27, 223–246 (2004). https://doi.org/10.1023/B:COAP.0000013057.54647.6d

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  • DOI: https://doi.org/10.1023/B:COAP.0000013057.54647.6d

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