Journal of Global Optimization

, Volume 53, Issue 1, pp 29–51 | Cite as

On linear programs with linear complementarity constraints

  • Jing Hu
  • John E. Mitchell
  • Jong-Shi Pang
  • Bin Yu


The paper is a manifestation of the fundamental importance of the linear program with linear complementarity constraints (LPCC) in disjunctive and hierarchical programming as well as in some novel paradigms of mathematical programming. In addition to providing a unified framework for bilevel and inverse linear optimization, nonconvex piecewise linear programming, indefinite quadratic programs, quantile minimization, and 0 minimization, the LPCC provides a gateway to a mathematical program with equilibrium constraints, which itself is an important class of constrained optimization problems that has broad applications. We describe several approaches for the global resolution of the LPCC, including a logical Benders approach that can be applied to problems that may be infeasible or unbounded.


Linear programs with linear complementarity constraints Inverse programming Hierarchical programming Piecewise linear programming Quantile minimization Cross-validated support vector regression 


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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  • Jing Hu
    • 1
  • John E. Mitchell
    • 2
  • Jong-Shi Pang
    • 3
  • Bin Yu
    • 4
  1. 1.Market Analytics, Inc.EvanstonUSA
  2. 2.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA
  3. 3.Department of Industrial and Enterprise Systems EngineeringUniversity of IllinoisUrbanaUSA
  4. 4.Department of Decision Sciences and Engineering SystemsRensselaer Polytechnic InstituteTroyUSA

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