Journal of Global Optimization

, Volume 62, Issue 2, pp 263–297 | Cite as

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



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.


Mathematical program with complementarity constraints Bi-parametric program Domain partitioning Global optimization algorithm 



Thanks to Dr. Bin Yu for his valuable comments on the numerical experiments.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Yu-Ching Lee
    • 1
  • Jong-Shi Pang
    • 2
  • John E. Mitchell
    • 3
  1. 1.Department of Industrial and Enterprise Systems EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Daniel J Epstein Department of Industrial and Systems EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  3. 3.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA

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