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IASI Research Report n. 607 (Next) Giampaolo Liuzzi,

Lucidi S.,

Marco SciandroneA derivative-free algorithm for linearly constrained finite minimax problemsABSTRACT In this paper we propose a new derivative-free algorithm for linearly constrained finite minimax problems. As it is well-known, standard derivative-free algorithms manage to locate points which only satisfy weak necessary optimality conditions for such a class of nonsmooth problems. In this work we define a new derivative-free algorithm globally converging toward standard stationary points for 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 depending on the sampling stepsize. We show also that the proposed approach can be used for defining derivative-free algorithms for general constrained minimization problems. Finally, we report numerical results on a set of standard test problems.