Ruziyeva, A.; Dempe, S. Optimality conditions in nondifferentiable fuzzy optimization. (English) Zbl 1342.90230 Optimization 64, No. 2, 349-363 (2015). The study is concerned with a class of nondifferentiable fuzzy optimization problems described in the following form \[ f(x)\to \text{Min},\qquad g(x)\leq 0, \] where the objective function \(f\) assumes fuzzy values by mapping \(\mathbb{R}^n\) to the space of fuzzy numbers and the constraint \(g: \mathbb{R}^n\to\mathbb{R}^k\) is a numeric mapping. The nondifferentiability of the problem stems from the fact that objective function or constraints are nondifferentiable. The objective function is described by a collection of \(\alpha\)-cuts. A set of optimal solutions to the fuzzy optimization problem is presented through the set of Pareto optimal solutions of the corresponding bicriterial optimization problem. The question of local optimality of the optimal solution is discussed. Necessary and sufficient optimality conditions for the solution to the nondiferentiable fuzzy optimization problem are also provided. An illustrative numeric example is presented as well. Reviewer: Witold Pedrycz (Edmonton) Cited in 6 Documents MSC: 90C70 Fuzzy and other nonstochastic uncertainty mathematical programming 90C46 Optimality conditions and duality in mathematical programming 90C30 Nonlinear programming Keywords:nondifferentiable optimization; necessary and sufficient conditions; nondifferentiable fuzzy function; Pareto optimal solution PDFBibTeX XMLCite \textit{A. Ruziyeva} and \textit{S. Dempe}, Optimization 64, No. 2, 349--363 (2015; Zbl 1342.90230) Full Text: DOI References: [1] DOI: 10.1016/S0019-9958(65)90241-X · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X [2] Dempe S, Methods of multicriteria decision – theory and applications pp 29– (2009) [3] Orlovski SA, Management decision support systems using fuzzy sets and possibility theory pp 136– (1985) [4] DOI: 10.1016/j.ejor.2006.12.053 · Zbl 1176.90679 · doi:10.1016/j.ejor.2006.12.053 [5] DOI: 10.1080/02331930410001699928 · Zbl 1144.90528 · doi:10.1080/02331930410001699928 [6] DOI: 10.1016/j.ejor.2005.09.007 · Zbl 1137.90712 · doi:10.1016/j.ejor.2005.09.007 [7] DOI: 10.1080/02331930601120037 · Zbl 1191.90093 · doi:10.1080/02331930601120037 [8] DOI: 10.1016/0165-0114(89)90134-6 · Zbl 0662.90045 · doi:10.1016/0165-0114(89)90134-6 [9] Rockafellar R, Convex analysis (1970) · Zbl 0932.90001 · doi:10.1515/9781400873173 [10] DOI: 10.1016/0377-2217(95)00055-0 · Zbl 1006.90506 · doi:10.1016/0377-2217(95)00055-0 [11] DOI: 10.1016/j.fss.2011.07.014 · Zbl 1238.90142 · doi:10.1016/j.fss.2011.07.014 [12] DOI: 10.1007/978-94-015-7949-0 · doi:10.1007/978-94-015-7949-0 [13] Ehrgott M, Multicriteria optimization (2005) [14] Chanas S, Fuzzy optimization pp 148– (1994) [15] DOI: 10.1109/TAC.1963.1105511 · doi:10.1109/TAC.1963.1105511 [16] DOI: 10.1137/060677513 · Zbl 1167.90020 · doi:10.1137/060677513 [17] DOI: 10.1007/s001860300316 · Zbl 1131.90054 · doi:10.1007/s001860300316 [18] DOI: 10.1023/A:1023993231971 · Zbl 1118.90316 · doi:10.1023/A:1023993231971 [19] DOI: 10.1016/0377-2217(90)90375-L · Zbl 0718.90079 · doi:10.1016/0377-2217(90)90375-L [20] DOI: 10.1016/S0377-2217(99)00319-7 · Zbl 0991.90080 · doi:10.1016/S0377-2217(99)00319-7 [21] DOI: 10.1007/s10700-005-4916-y · Zbl 1176.90076 · doi:10.1007/s10700-005-4916-y [22] Clarke FH, Optimization and nonsmooth analysis (1983) 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.