Heuristic pattern search for bound constrained minimax problems
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
A derivative-free approximate gradient sampling algorithm for finite minimax problems
Computational Optimization and Applications
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In this paper we propose a new derivative-free algorithm for linearly constrained finite minimax problems. Due to the nonsmoothness of this class of problems, standard derivative-free algorithms can locate only points which satisfy weak necessary optimality conditions. In this work we define a new derivative-free algorithm which is globally convergent toward standard stationary points of the finite minimax problem. To this end, we convert the original problem into a smooth one by using a smoothing technique based on the exponential penalty function of Kort and Bertsekas. This technique depends on a smoothing parameter which controls the approximation to the finite minimax problem. The proposed method is based on a sampling of the smooth function along a suitable search direction and on a particular updating rule for the smoothing parameter that depends on the sampling stepsize. Numerical results on a set of standard minimax test problems are reported.