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

Francisco Jara-Moroni; Jong Shi Pang; Andreas Wächter

doi:10.1007/s10107-017-1208-6

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

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	221-254
Number of pages	34
Journal	Mathematical Programming
Volume	169
Issue number	1
DOIs	https://doi.org/10.1007/s10107-017-1208-6
State	Published - 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

Access to Document

10.1007/s10107-017-1208-6

Cite this

@article{6fa39d706feb47959e3b9e79297bccbc,

title = "A study of the difference-of-convex approach for solving linear programs with complementarity constraints",

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.",

keywords = "Bilevel programming, Complementarity constraints, Difference-of-convex, Penalty functions",

author = "Francisco Jara-Moroni and Pang, {Jong Shi} and Andreas W{\"a}chter",

note = "Publisher Copyright: {\textcopyright} 2017, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society.",

year = "2018",

month = may,

day = "1",

doi = "10.1007/s10107-017-1208-6",

language = "English (US)",

volume = "169",

pages = "221--254",

journal = "Mathematical Programming",

issn = "0025-5610",

publisher = "Springer-Verlag GmbH and Co. KG",

number = "1",

}

TY - JOUR

T1 - A study of the difference-of-convex approach for solving linear programs with complementarity constraints

AU - Jara-Moroni, Francisco

AU - Pang, Jong Shi

AU - Wächter, Andreas

PY - 2018/5/1

Y1 - 2018/5/1

N2 - 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.

AB - 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.

KW - Bilevel programming

KW - Complementarity constraints

KW - Difference-of-convex

KW - Penalty functions

UR - http://www.scopus.com/inward/record.url?scp=85033701299&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85033701299&partnerID=8YFLogxK

U2 - 10.1007/s10107-017-1208-6

DO - 10.1007/s10107-017-1208-6

M3 - Article

AN - SCOPUS:85033701299

SN - 0025-5610

VL - 169

SP - 221

EP - 254

JO - Mathematical Programming

JF - Mathematical Programming

IS - 1

ER -

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

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this