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A hybrid algorithm for linearly constrained minimax problems

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  • Fusheng Wang

Abstract

Many real life problems can be stated as a minimax problem, such as economics, finance, management, engineering and other fields, which demonstrate the importance of having reliable methods to tackle minimax problems. In this paper, an algorithm for linearly constrained minimax problems is presented in which we combine the trust-region methods with the line-search methods and curve-search methods. By means of this hybrid technique, it avoids possibly solving the trust-region subproblems many times, and make better use of the advantages of different methods. Under weaker conditions, the global and superlinear convergence are achieved. Numerical experiments show that the new algorithm is robust and efficient. Copyright Springer Science+Business Media New York 2013

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  • Fusheng Wang, 2013. "A hybrid algorithm for linearly constrained minimax problems," Annals of Operations Research, Springer, vol. 206(1), pages 501-525, July.
    • Handle: RePEc:spr:annopr:v:206:y:2013:i:1:p:501-525:10.1007/s10479-012-1274-3
    DOI: 10.1007/s10479-012-1274-3
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    References listed on IDEAS

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    1. Wenyu Sun & Ya-xiang Yuan, 2001. "A Conic Trust-Region Method for Nonlinearly Constrained Optimization," Annals of Operations Research, Springer, vol. 103(1), pages 175-191, March.
    2. Y.H. Yu & L. Gao, 2002. "Nonmonotone Line Search Algorithm for Constrained Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 419-446, November.
    3. K.L. Teo & X.Q. Yang, 2001. "Portfolio Selection Problem with Minimax Type Risk Function," Annals of Operations Research, Springer, vol. 101(1), pages 333-349, January.
    4. Tammy Drezner, 2009. "Location of retail facilities under conditions of uncertainty," Annals of Operations Research, Springer, vol. 167(1), pages 107-120, March.
    5. Rustem, Berc & Becker, Robin G. & Marty, Wolfgang, 2000. "Robust min-max portfolio strategies for rival forecast and risk scenarios," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1591-1621, October.
    6. Fusheng Wang & Kecun Zhang, 2008. "A hybrid algorithm for nonlinear minimax problems," Annals of Operations Research, Springer, vol. 164(1), pages 167-191, November.
    7. Oded Berman & Jiamin Wang & Zvi Drezner & George Wesolowsky, 2003. "A Probabilistic Minimax Location Problem on the Plane," Annals of Operations Research, Springer, vol. 122(1), pages 59-70, September.
    8. Igor Averbakh & Oded Berman, 2002. "Minmax p-Traveling Salesmen Location Problems on a Tree," Annals of Operations Research, Springer, vol. 110(1), pages 55-68, February.
    9. C. Michelot & F. Plastria, 2002. "An Extended Multifacility Minimax Location Problem Revisited," Annals of Operations Research, Springer, vol. 111(1), pages 167-179, March.
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    Cited by:

    1. Jin-bao Jian & Qing-juan Hu & Chun-ming Tang, 2014. "Superlinearly Convergent Norm-Relaxed SQP Method Based on Active Set Identification and New Line Search for Constrained Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 859-883, December.

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