A study of the difference-of-convex approach for solving linear programs with complementarity constraints

This paper studies the difference-of-convex (DC) penalty formulations and the associated difference-of-convex algorithm (DCA) for computing stationary solutions of linear programs with complementarity constraints (LPCCs). We focus on three such formulations and establish connections between their st...

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Bibliographic Details
Published in:Mathematical programming 2018-05, Vol.169 (1), p.221-254
Main Authors: Jara-Moroni, Francisco, Pang, Jong-Shi, Wächter, Andreas
Format: Article
Language:English
Subjects:
Algorithms
Calculus of Variations and Optimal Control
Optimization
Combinatorics
Formulations
Full Length Paper
Integer programming
Linear programming
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Nonlinear programming
Numerical Analysis
Theoretical
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Summary:This paper studies the difference-of-convex (DC) penalty formulations and the associated difference-of-convex algorithm (DCA) for computing stationary solutions of linear programs with complementarity constraints (LPCCs). We focus on three such formulations and establish connections between their stationary solutions and those of the LPCC. Improvements of the DCA are proposed to remedy some drawbacks in a straightforward adaptation of the DCA to these formulations. Extensive numerical results, including comparisons with an existing nonlinear programming solver and the mixed-integer formulation, are presented to elucidate the effectiveness of the overall DC approach.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-017-1208-6