Abstract
In this paper, we propose pattern search methods for finite minimax problems. Due to the nonsmoothness of this class of problems, we convert the original problem into a smooth one by using a smoothing technique based on the exponential penalty function of Kort and Bertsekas, which technique depends on a smoothing parameter that control the approximation to the finite minimax problems. The proposed methods are based on a sampling of the smooth function along a set of suitable search directions and on an updating rule for the step-control parameter. Under suitable conditions, we get the global convergence results despite the fact that pattern search methods do not have explicit information concerning the gradient and consequently are unable to enforce explicitly a notion of sufficient feasible decrease.
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Ma, J., Zhang, X. Pattern search methods for finite minimax problems. J. Appl. Math. Comput. 32, 491–506 (2010). https://doi.org/10.1007/s12190-009-0266-1
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DOI: https://doi.org/10.1007/s12190-009-0266-1