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A comparison of solution approaches for the numerical treatment of or-constrained optimization problems

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  • Patrick Mehlitz

    (Brandenburgische Technische Universität Cottbus–Senftenberg)

Abstract

Mathematical programs with or-constraints form a new class of disjunctive optimization problems with inherent practical relevance. In this paper, we provide a comparison of three different solution methods for the numerical treatment of this problem class which are inspired by classical approaches from disjunctive programming. First, we study the replacement of the or-constraints as nonlinear inequality constraints using suitable NCP-functions. Second, we transfer the or-constrained program into a mathematical program with switching or complementarity constraints which can be treated with the aid of well-known relaxation methods. Third, a direct Scholtes-type relaxation of the or-constraints is investigated. A numerical comparison of all these approaches which is based on three essentially different model programs from or-constrained optimization closes the paper.

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  • Patrick Mehlitz, 2020. "A comparison of solution approaches for the numerical treatment of or-constrained optimization problems," Computational Optimization and Applications, Springer, vol. 76(1), pages 233-275, May.
    • Handle: RePEc:spr:coopap:v:76:y:2020:i:1:d:10.1007_s10589-020-00169-z
    DOI: 10.1007/s10589-020-00169-z
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    References listed on IDEAS

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    1. M.L. Flegel & C. Kanzow, 2005. "Abadie-Type Constraint Qualification for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 124(3), pages 595-614, March.
    2. Sven Leyffer, 2006. "Complementarity constraints as nonlinear equations: Theory and numerical experience," Springer Optimization and Its Applications, in: Stephan Dempe & Vyacheslav Kalashnikov (ed.), Optimization with Multivalued Mappings, pages 169-208, Springer.
    3. C. Kanzow & N. Yamashita & M. Fukushima, 1997. "New NCP-Functions and Their Properties," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 115-135, July.
    4. John N. Hooker, 2002. "Logic, Optimization, and Constraint Programming," INFORMS Journal on Computing, INFORMS, vol. 14(4), pages 295-321, November.
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