Second-order optimality conditions for efficiency in C1,1-smooth quasiconvex multiobjective programming problem

This paper deals with a quasiconvex multiobjective programming problem with inequality and set constraints with C-1,C-1-smooth data. Based on the definition of quasiconvexity, pseudoconvexity and second-order Mordukhovich/Frechet subdifferentials of extended-real-valued function, we propose the two generalized Ben-Tal second-order constraint qualifications and then establish strong and weak Karush-Kuhn-Tucker type second-order necessary optimality conditions for weak efficiency to such problem. Under some suitable assumptions on the pseudoconvexity and C-1,C-1-around a feasible solution of objective and constraint functions, some second-order sufficient optimality conditions in terms of Frechet subdifferentials are presented. An application of the result on sufficient optimality of order two in terms of Mordukhovich subdifferentials in the sense of the functions belong to C-2-around a feasible solution is obtained. Some examples are also provided to demonstrate for our findings.