Bagirov, A. M.; Nuaimat, A. Al; Sultanova, N. Hyperbolic smoothing function method for minimax problems. (English) Zbl 1282.65065 Optimization 62, No. 6, 759-782 (2013). The authors present an approach for solving finite minimax problems that is based on the use of a hyperbolic smoothing function. The properties of the hyperbolic smoothing function are investigated. Some preliminary numerical results are reported to compare the performance of the proposed method with those obtained using exponential smoothing functions. Reviewer: Guoqiang Wang (Shanghai) Cited in 19 Documents MSC: 65K05 Numerical mathematical programming methods 90C47 Minimax problems in mathematical programming Keywords:minimax problem; nonsmooth optimization; smoothing techniques; subdifferential; numerical results PDFBibTeX XMLCite \textit{A. M. Bagirov} et al., Optimization 62, No. 6, 759--782 (2013; Zbl 1282.65065) Full Text: DOI References: [1] DOI: 10.1080/10556780903151565 · Zbl 1202.65072 · doi:10.1080/10556780903151565 [2] DOI: 10.1007/s10957-007-9335-5 · Zbl 1165.90021 · doi:10.1007/s10957-007-9335-5 [3] Ben-Tal A, Lecture Notes in Mathematics 1405 pp 1– (1989) [4] Demyanov VF, Introduction to Minimax (1974) [5] DOI: 10.1007/s101070100263 · Zbl 1049.90004 · doi:10.1007/s101070100263 [6] DOI: 10.1007/978-1-4613-3557-3 · doi:10.1007/978-1-4613-3557-3 [7] Hiriart-Urruty JB, Convex Analysis and Minimization Algorithms, Vols 1 and 2 (1993) [8] Kiwiel KC, Methods of Descent for Nondifferentiable Optimization, Lecture Notes in Mathematics (1985) · Zbl 0561.90059 · doi:10.1007/BFb0074500 [9] Lukśan L, Test problems for nonsmooth unconstrained and linearly constrained optimization (2000) [10] Mäkelä MM, Nonsmooth Optimization (1992) · doi:10.1142/1493 [11] DOI: 10.1023/B:JOTA.0000006685.60019.3e · Zbl 1061.90117 · doi:10.1023/B:JOTA.0000006685.60019.3e [12] DOI: 10.1007/s10957-008-9355-9 · Zbl 1211.90283 · doi:10.1007/s10957-008-9355-9 [13] Smale, S. 1986.Algorithms for Solving Equations, Proceedings of the International Congress of Mathematicians, 172–195. CA, USA: Berkeley. [14] DOI: 10.1007/s11590-008-0090-9 · Zbl 1154.90619 · doi:10.1007/s11590-008-0090-9 [15] DOI: 10.1023/A:1010924609000 · Zbl 0997.90081 · doi:10.1023/A:1010924609000 [16] Xavier AE, Penalizaćao hiperbólica (1982) [17] DOI: 10.1016/j.patcog.2009.06.018 · Zbl 1187.68514 · doi:10.1016/j.patcog.2009.06.018 [18] DOI: 10.1007/s10898-004-0737-8 · Zbl 1093.90023 · doi:10.1007/s10898-004-0737-8 [19] DOI: 10.1016/j.amc.2009.11.034 · Zbl 1194.65083 · doi:10.1016/j.amc.2009.11.034 [20] DOI: 10.1023/A:1011211101714 · Zbl 1054.90087 · doi:10.1023/A:1011211101714 [21] DOI: 10.1016/j.amc.2007.10.070 · Zbl 1146.65053 · doi:10.1016/j.amc.2007.10.070 [22] DOI: 10.1007/BF01581628 · Zbl 0468.90064 · doi:10.1007/BF01581628 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.