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Algorithms with Adaptive Smoothing for Finite Minimax Problems

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Abstract

We present a new feedback precision-adjustment rule for use with a smoothing technique and standard unconstrained minimization algorithms in the solution of finite minimax problems. Initially, the feedback rule keeps a precision parameter low, but allows it to grow as the number of iterations of the resulting algorithm goes to infinity. Consequently, the ill-conditioning usually associated with large precision parameters is considerably reduced, resulting in more efficient solution of finite minimax problems.

The resulting algorithms are very simple to implement, and therefore are particularly suitable for use in situations where one cannot justify the investment of time needed to retrieve a specialized minimax code, install it on one's platform, learn how to use it, and convert data from other formats. Our numerical tests show that the algorithms are robust and quite effective, and that their performance is comparable to or better than that of other algorithms available in the Matlab environment.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, University of California, Berkeley, California

    E. Polak (Professor)

  2. Department of Civil and Environmental Engineering, University of California, Berkeley, California

    J. O. Royset (Graduate Student)

  3. School of Mathematics, University of New South Wales, Sydney, Australia

    R. S. Womersley (Associate Professor)

Authors
  1. E. Polak
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  2. J. O. Royset
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  3. R. S. Womersley
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Polak, E., Royset, J.O. & Womersley, R.S. Algorithms with Adaptive Smoothing for Finite Minimax Problems. Journal of Optimization Theory and Applications 119, 459–484 (2003). https://doi.org/10.1023/B:JOTA.0000006685.60019.3e

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  • DOI: https://doi.org/10.1023/B:JOTA.0000006685.60019.3e

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