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A Study of the Difference-of-Convex Approach for Solving Linear Programs with Complementarity Constraints

Francisco Jara-Moroni(franciscojaramoroni2013***at***u.northwestern.edu)
Jong-Shi Pang(jongship***at***usc.edu )
Andreas Wächter(andreas.waechter***at***northwestern.edu )

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: Complementarities, MPCC, LPCC, DCA

Category 1: Complementarity and Variational Inequalities

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )


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Entry Submitted: 08/29/2016
Entry Accepted: 09/01/2016
Entry Last Modified: 08/29/2016

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