Optimality conditions and duality in nonsmooth multiobjective optimization problems

• Published in: Annals of operations research Vol. 217; no. 1; pp. 117 - 136
• Main Authors: Chuong, Thai Doan, Kim, Do Sang
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.06.2014; Springer; Springer Nature B.V
• Subjects: Approximation; Business and Management; Combinatorics; Constraining; Differential equations; Fuzzy; Fuzzy logic; Fuzzy set theory; Inequalities; Inequalities (Mathematics); Mathematical functions; Mathematical optimization; Mathematical research; Operations research; Operations Research/Decision Theory; Optimization; Studies; Sum rules; Theory of Computation; 49K99; Limiting subdifferential; 90C46; Multiobjective optimization; Optimality condition; 65K10; 90C29; Duality; invex-infine function; The (KKT) condition
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-014-1552-3

Exploiting some tools of modern variational analysis involving the approximate extremal principle, the fuzzy sum rule for the Fréchet subdifferential, the sum rule for the limiting subdifferential and the scalarization formulae of the coderivatives, we establish necessary conditions for (weakly) efficient solutions of a multiobjective optimization problem with inequality and equality constraints. Sufficient conditions for (weakly) efficient solutions of an aforesaid problem are also provided by means of employing L -(strictly) invex-infine functions defined in terms of the limiting subdifferential. In addition, we introduce types of Wolfe and Mond–Weir dual problems and investigate weak/strong duality relations.