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On Complexity of the Translational-Cut Algorithm for Convex Minimax Problems

Author

Listed:
  • K. A. Ariyawansa

    (Washington State University)

  • P. L. Jiang

    (Delta Dental Plan of Minnesota)

Abstract

Burke, Goldstein, Tseng, and Ye (Ref. 1) have presented an interesting interior-point algorithm for a class of smooth convex minimax problems. They have also presented a complexity analysis leading to a worst-case bound on the total work necessary to obtain a solution within a prescribed tolerance. In this paper, we present refinements to the analysis of Burke et al. which show that the resulting complexity bound can be worse than those for other algorithms available at the time Ref. 1 was published.

Suggested Citation

  • K. A. Ariyawansa & P. L. Jiang, 2000. "On Complexity of the Translational-Cut Algorithm for Convex Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 223-243, November.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:2:d:10.1023_a:1026422013954
    DOI: 10.1023/A:1026422013954
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    References listed on IDEAS

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    1. Robert G. Bland & Donald Goldfarb & Michael J. Todd, 1981. "Feature Article—The Ellipsoid Method: A Survey," Operations Research, INFORMS, vol. 29(6), pages 1039-1091, December.
    2. Kurt M. Anstreicher, 1997. "On Vaidya's Volumetric Cutting Plane Method for Convex Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 63-89, February.
    3. Robert Mifflin, 1975. "Subproblem and Overall Convergence for a Method-of-Centers Algorithm," Operations Research, INFORMS, vol. 23(4), pages 796-809, August.
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    Cited by:

    1. E. Y. Pee & J. O. Royset, 2011. "On Solving Large-Scale Finite Minimax Problems Using Exponential Smoothing," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 390-421, February.

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