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Solving Disjunctive Optimization Problems by Generalized Semi-infinite Optimization Techniques

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  • Peter Kirst

    (Karlsruhe Institute of Technology (KIT))

  • Oliver Stein

    (Karlsruhe Institute of Technology (KIT))

Abstract

We describe a new possibility to model disjunctive optimization problems as generalized semi-infinite programs. In contrast to existing methods in disjunctive programming, our approach does not expect any special formulation of the underlying logical expression. Applying existing lower-level reformulations for the corresponding semi-infinite program, we derive conjunctive nonlinear problems without any logical expressions, which can be locally solved by standard nonlinear solvers. Our preliminary numerical results on some small-scale examples indicate that our reformulation procedure is a reasonable method to solve disjunctive optimization problems.

Suggested Citation

  • Peter Kirst & Oliver Stein, 2016. "Solving Disjunctive Optimization Problems by Generalized Semi-infinite Optimization Techniques," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1079-1109, June.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:3:d:10.1007_s10957-016-0862-9
    DOI: 10.1007/s10957-016-0862-9
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    References listed on IDEAS

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    1. Holger Scheel & Stefan Scholtes, 2000. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 1-22, February.
    2. H. T. Jongen & J. J. Rückmann & O. Stein, 1997. "Disjunctive Optimization: Critical Point Theory," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 321-336, May.
    3. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    4. Stein, Oliver & Still, Georg, 2002. "On generalized semi-infinite optimization and bilevel optimization," European Journal of Operational Research, Elsevier, vol. 142(3), pages 444-462, November.
    5. M. Diehl & B. Houska & O. Stein & P. Steuermann, 2013. "A lifting method for generalized semi-infinite programs based on lower level Wolfe duality," Computational Optimization and Applications, Springer, vol. 54(1), pages 189-210, January.
    6. O. Stein & A. Winterfeld, 2010. "Feasible Method for Generalized Semi-Infinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 419-443, August.
    7. Beaumont, Nicholas, 1990. "An algorithm for disjunctive programs," European Journal of Operational Research, Elsevier, vol. 48(3), pages 362-371, October.
    8. Stein, Oliver, 2012. "How to solve a semi-infinite optimization problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 312-320.
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    Cited by:

    1. Olga Kostyukova & Tatiana Tchemisova, 2017. "Optimality Conditions for Convex Semi-infinite Programming Problems with Finitely Representable Compact Index Sets," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 76-103, October.
    2. Peter Kirst & Fabian Rigterink & Oliver Stein, 2017. "Global optimization of disjunctive programs," Journal of Global Optimization, Springer, vol. 69(2), pages 283-307, October.

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