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

7 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

Keywords

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

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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