An Adaptive Smoothing Method for Continuous Minimax Problems

Hongxia Yin ()
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Hongxia Yin: Department of Mathematics and Statistics, Minnesota State University Mankato, Mankato, MN 56001, USA;

Asia-Pacific Journal of Operational Research (APJOR), 2015, vol. 32, issue 01, 1-19

Abstract: A simple and implementable two-loop smoothing method for semi-infinite minimax problem is given with the discretization parameter and the smoothing parameter being updated adaptively. We prove the global convergence of the algorithm when the steepest descent method or a BFGS type quasi-Newton method is applied to the smooth subproblems. The strategy for updating the smoothing parameter can not only guarantee the convergence of the algorithm but also considerably reduce the ill-conditioning caused by increasing the value of the smoothing parameter. Numerical tests show that the algorithm is robust and effective.

Keywords: Semi-infinite continuous minimax problem; smoothing method; cautious BFGS method; steepest descent method; global convergence; polynomial interpolation (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0217595915400011

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