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

Francisco Jara-Moroni, Jong Shi Pang, Andreas Wächter*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)221-254
Number of pages34
JournalMathematical Programming
Volume169
Issue number1
DOIs
StatePublished - May 1 2018

Funding

The first and third author were supported in part by the U.S. National Science Foundation Grant CMMI-1334639. The second author was partially supported by the U.S. National Science Foundation Grant CMMI-1402052 and the Air Force Office of Sponsored Research Grant FA9550-15-1-0126.

Keywords

  • Bilevel programming
  • Complementarity constraints
  • Difference-of-convex
  • Penalty functions

ASJC Scopus subject areas

  • Software
  • General Mathematics

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