Second-Order Optimality Conditions for Efficiency in C1-Smooth Robustly Quasiconvex Multiobjective Programming Problems

We study some second-order optimality conditions in terms of second-order Mordukhovich's subdifferentials for the weak efficiency of C-1 -smooth robustly quasiconvex multiobjective programming problem with set, inequality and equality constraints. We provide some second- order generalized constraint qualifications and two necessary conditions for the robust quasiconvexity of C-1 -smooth/ C-1,C-1 -smooth mappings. Using this result, weak and strong second-order Karush-Kuhn-Tuckertype necessary optimality conditions in terms of Mordukhovich's subdifferentials / Fr & eacute;chet's subdifferentials are provided. Under some suitable assumptions, some second-order Karush-Kuhn-Tucker type sufficient optimality conditions are presented too. Examples demonstrate the applicability of the obtained results.