Algorithms with Adaptive Smoothing for Finite Minimax Problems

E. Polak, J. O. Royset and R. S. Womersley
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E. Polak: University of California
J. O. Royset: University of California
R. S. Womersley: University of New South Wales

Journal of Optimization Theory and Applications, 2003, vol. 119, issue 3, No 2, 459-484

Abstract: 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.

Keywords: Finite minimax; nonsmooth optimization algorithms; smoothing techniques; feedback precision-adjustment rule (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (15)

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DOI: 10.1023/B:JOTA.0000006685.60019.3e

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