Optimality conditions and duality in nonsmooth multiobjective optimization problems

摘要

Exploiting some tools of modern variational analysis involving the approximate extremal principle, the fuzzy sum rule for the Frechet 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.