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 / $C^{1,1}$-smooth mappings. Using this result, weak and strong second-order Karush-Kuhn-Tucker-type necessary optimality conditions in terms of Mordukhovich's subdifferentials / Fréchet'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.