A study of the difference-of-convex approach for solving linear programs with complementarity constraints
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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.
KeywordsDifference-of-convex Complementarity constraints Penalty functions Bilevel programming
Mathematics Subject Classification90C05 Linear programming 90C30 Nonlinear programming 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions)
We thank a referee for very helpful comments that have improved the presentation of the paper.
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