On higher-order strong KKT optimality conditions for multiobjective semi-infinite programming problems

This paper is intended to study higher-order necessary optimality conditions for multiobjective semi-infinite programming problems, in which the objective and constraint functions are considered to be m-stable at a reference point. Two data qualifications, called the weak Abadie data qualification (WADQ) and the strong Su–Luu data qualification (SSLDQ), are introduced in terms of mth-order upper Studniarski derivatives. The mth-order strong KKT necessary optimality conditions for a local weakly efficient solution are presented under the WADQ and the SSLDQ. Additionally, if the reference point is further a local Borwein-properly efficient solution, the mth-order strong KKT necessary optimality conditions are satisfied without requiring the assumption of SSLDQ.