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Global optimization of disjunctive programs

Author

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  • Peter Kirst

    (Karlsruhe Institute of Technology)

  • Fabian Rigterink

    (The University of Newcastle)

  • Oliver Stein

    (Karlsruhe Institute of Technology)

Abstract

We propose a new branch-and-bound framework for global optimization of disjunctive programs with general logical expressions. We do not assume the logical expressions to be in any normal form, and, under slightly stronger assumptions, we allow the use of negations and implications. In contrast to the widely used reformulation as a mixed-integer program, we compute the lower bounds and evaluate the logical expression in one step. Thus, we reduce the size of the problem and work exclusively with continuous variables, which is computationally advantageous. We present preliminary numerical results as proof of concept.

Suggested Citation

  • Peter Kirst & Fabian Rigterink & Oliver Stein, 2017. "Global optimization of disjunctive programs," Journal of Global Optimization, Springer, vol. 69(2), pages 283-307, October.
    • Handle: RePEc:spr:jglopt:v:69:y:2017:i:2:d:10.1007_s10898-017-0526-9
    DOI: 10.1007/s10898-017-0526-9
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    References listed on IDEAS

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    1. Ruiz, Juan P. & Grossmann, Ignacio E., 2012. "A hierarchy of relaxations for nonlinear convex generalized disjunctive programming," European Journal of Operational Research, Elsevier, vol. 218(1), pages 38-47.
    2. 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.
    3. Sawaya, Nicolas & Grossmann, Ignacio, 2012. "A hierarchy of relaxations for linear generalized disjunctive programming," European Journal of Operational Research, Elsevier, vol. 216(1), pages 70-82.
    4. 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.
    5. Peter Kirst & Oliver Stein & Paul Steuermann, 2015. "Deterministic upper bounds for spatial branch-and-bound methods in global minimization with nonconvex constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 591-616, July.
    6. Beaumont, Nicholas, 1990. "An algorithm for disjunctive programs," European Journal of Operational Research, Elsevier, vol. 48(3), pages 362-371, October.
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    Cited by:

    1. Yinrun Lyu & Li Chen & Changyou Zhang & Dacheng Qu & Nasro Min-Allah & Yongji Wang, 2018. "An interleaved depth-first search method for the linear optimization problem with disjunctive constraints," Journal of Global Optimization, Springer, vol. 70(4), pages 737-756, April.
    2. Max Bucher & Alexandra Schwartz, 2018. "Second-Order Optimality Conditions and Improved Convergence Results for Regularization Methods for Cardinality-Constrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 383-410, August.
    3. Peter Kirst & Oliver Stein, 2019. "Global optimization of generalized semi-infinite programs using disjunctive programming," Journal of Global Optimization, Springer, vol. 73(1), pages 1-25, January.

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