SDMINMAX swMATH ID: 36992 Software Authors: Liuzzi, G.; Lucidi, S.; Sciandrone, M. Description: DFL - A Derivative-Free Library - SDMINMAX: A derivative-free algorithm for linearly constrained finite minimax problems. 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 exponentialpenalty 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. Homepage: http://www.iasi.cnr.it/~liuzzi/DFL/index.php/list3/13-nonsmooth-optimization-and-minimax-problems/15-sdminmax Dependencies: Fortran90 Keywords: derivative-free optimization; linearly constrained finite minimax problems; non-smooth optimization Related Software: DFLBOX; DFL; SDPEN; DFBOX_IMPR; DGM; SDBOX; KELLEY; IMFIL; BOBYQA; DFO; NOMAD; GradSamp; CUTEr; OrthoMADS; APPSPACK; DFN; MultiGLODS; DeepHyper; DFMO; MOIF Cited in: 12 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A derivative-free algorithm for linearly constrained finite minimax problems. Zbl 1131.90074Liuzzi, G.; Lucidi, S.; Sciandrone, M. 2006 all top 5 Cited by 28 Authors 4 Liuzzi, Giampaolo 3 Lucidi, Stefano 1 Casolino, Giovanni Mercurio 1 Ciccazzo, Angelo 1 Gao, Jing 1 Hare, W. 1 He, Suxiang 1 Jian, Jinbao 1 Larson, Jeffrey 1 Latorre, Vittorio 1 Li, Guoyin 1 Li, Yanxi 1 Lin, He 1 Losi, Arturo 1 Lv, Wei 1 Menickelly, Matt 1 Nutini, Julie 1 Rinaldi, Francesco 1 Sciandrone, Marco 1 Sui, Ruirui 1 Sun, Qiang 1 Tang, Chunming 1 Tawhid, Mohamed Aly 1 Wild, Stefan M. 1 Yang, Li 1 Yu, Bo 1 Zhou, Shumin 1 Zhu, Detong all top 5 Cited in 11 Serials 2 Optimization Letters 1 Applied Mathematics and Computation 1 Journal of Optimization Theory and Applications 1 Journal of Global Optimization 1 SIAM Journal on Optimization 1 Computational Optimization and Applications 1 Optimization and Engineering 1 Journal of Systems Science and Complexity 1 Acta Numerica 1 Journal of Industrial and Management Optimization 1 East Asian Journal on Applied Mathematics Cited in 5 Fields 12 Operations research, mathematical programming (90-XX) 3 Numerical analysis (65-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Computer science (68-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year