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An algorithm for global solution to bi-parametric linear complementarity constrained linear programs

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  • Yu-Ching Lee
  • Jong-Shi Pang
  • John Mitchell

Abstract

A linear program with linear complementarity constraints (LPCC) is among the simplest mathematical programs with complementarity constraints. Yet the global solution of the LPCC remains difficult to find and/or verify. In this work we study a specific type of the LPCC which we term a bi-parametric LPCC. Reformulating the bi-parametric LPCC as a non-convex quadratically constrained program, we develop a domain-partitioning algorithm that solves a series of the linear subproblems and/or convex quadratically constrained subprograms obtained by the relaxations of the complementarity constraint. The choice of an artificial constants-pair allows us to control the domain on which the partitioning is done. Numerical results of robustly solving 105 randomly generated bi-parametric LPCC instances of different structures associated with different numbers of complementarity constraints by the algorithm are presented. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Yu-Ching Lee & Jong-Shi Pang & John Mitchell, 2015. "An algorithm for global solution to bi-parametric linear complementarity constrained linear programs," Journal of Global Optimization, Springer, vol. 62(2), pages 263-297, June.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:2:p:263-297
    DOI: 10.1007/s10898-014-0228-5
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    References listed on IDEAS

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