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Min-Max Optimization of Several Classical Discrete Optimization Problems

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  • G. Yu

    (University of Texas at Austin)

Abstract

In this paper, we study discrete optimization problems with min-max objective functions. This type of problems has direct applications in the recent development of robust optimization. The following well-known classes of problems are discussed: minimum spanning tree problem, resource allocation problem with separable cost functions, and production control problem. Computational complexities of the corresponding min-max version of the above-mentioned problems are analyzed. Pseudopolynomial algorithms for these problems are provided under certain conditions.

Suggested Citation

  • G. Yu, 1998. "Min-Max Optimization of Several Classical Discrete Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 98(1), pages 221-242, July.
    • Handle: RePEc:spr:joptap:v:98:y:1998:i:1:d:10.1023_a:1022601301102
    DOI: 10.1023/A:1022601301102
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    References listed on IDEAS

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    1. Pang, Jong-Shi & Chang-Sung, Yu, 1989. "A min-max resource allocation problem with substitutions," European Journal of Operational Research, Elsevier, vol. 41(2), pages 218-223, July.
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    4. Czuchra, Waldemar, 1986. "A graphical method to solve a maximin allocation problem," European Journal of Operational Research, Elsevier, vol. 26(2), pages 259-261, August.
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    6. Rachelle S. Klein & Hanan Luss & Uriel G. Rothblum, 1993. "Minimax Resource Allocation Problems with Resource-Substitutions Represented by Graphs," Operations Research, INFORMS, vol. 41(5), pages 959-971, October.
    7. Seymour Kaplan, 1974. "Application of Programs with Maximin Objective Functions to Problems of Optimal Resource Allocation," Operations Research, INFORMS, vol. 22(4), pages 802-807, August.
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    Cited by:

    1. V. Jeyakumar & J. Vicente-Pérez, 2014. "Dual Semidefinite Programs Without Duality Gaps for a Class of Convex Minimax Programs," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 735-753, September.
    2. Eduardo Conde, 2014. "A Minmax Regret Linear Regression Model Under Uncertainty in the Dependent Variable," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 573-596, February.
    3. Uhan, Nelson A., 2015. "Stochastic linear programming games with concave preferences," European Journal of Operational Research, Elsevier, vol. 243(2), pages 637-646.

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