Chuong, Thai Doan Optimality and duality for proper and isolated efficiencies in multiobjective optimization. (English) Zbl 1252.49018 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 76, 93-104 (2013). Summary: We use some advanced tools of variational analysis and generalized differentiation such as the nonsmooth version of Fermat’s rule, the limiting/Mordukhovich subdifferential of maximum functions, and the sum rules for the Fréchet subdifferential and for the limiting one to establish necessary conditions for (local) properly efficient solutions and (local) isolated minimizers of a multiobjective optimization problem involving inequality and equality constraints. Sufficient conditions for the existence of such solutions are also provided under assumptions of (local) convex/affine functions or \(L\)-invex-infine functions defined in terms of the limiting subdifferential of locally Lipschitz functions. In addition, we propose a type of Wolfe dual problems and examine weak/strong duality relations under \(L\)-invexity-infineness hypotheses. Cited in 6 Documents MSC: 49J52 Nonsmooth analysis 49K99 Optimality conditions 49N15 Duality theory (optimization) 65K10 Numerical optimization and variational techniques 90C29 Multi-objective and goal programming 90C46 Optimality conditions and duality in mathematical programming Keywords:optimality condition; duality; isolated minimizer; Mordukhovich subdifferential; \(L\)-invex-infine function; multiobjective optimization PDFBibTeX XMLCite \textit{T. D. Chuong}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 76, 93--104 (2013; Zbl 1252.49018) Full Text: DOI