On Linear Programs with Linear Complementarity Constraints

Accepted for publication in the Journal of Global Optimization, 53(1), pages 29-51, 2012.

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Authors:

Jing Hu
Market Analytics, Inc., 500 Davis Street, Suite 1001, Evanston, Illinois 60201.

John E. Mitchell
mitchj at rpi dot edu
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180-3590, U.S.A

Jong-Shi Pang
jspang at illinois dot edu
Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, 117 Transportation Bldg., 104 S. Mathews Ave., Urbana, IL 61801.

Bin Yu
yub at rpi dot edu
Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, Troy, New York 12180-3590, U.S.A

Abstract:

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 zero-norm 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.

Keywords: linear programs with linear complementarity constraints; LPECs; inverse programming; hierarchical programming; piecewise linear; quantile minimization; cross-validated support vector regression

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