On approximate optimality conditions for robust multi-objective convex optimization problems

In this paper, we are interested in the study of approximate optimality conditions for weakly ϵ-efficient solutions to robust multi-objective optimization problems ((RMOP) for short) in view of its associated minimax optimization problem (MMOP). To this end, we first establish the relationship between a weakly ϵ-efficient solution to the problem (RMOP) and an α-solution to the problem (MMOP), where ϵ=(ϵ1,…,ϵp)∈R+p∖{0} and α=maxj=1,…,p{ϵj}. Then, we explore the representation of the so-called β-normal set (where β≥ 0 is a given parameter) to a closed convex set at some reference point by two methods. At last, by employing the α-subdifferential of the max-function and the obtained representation of the β-normal set, we establish an approximate necessary optimality condition for the problem (RMOP). Moreover, we also give an example to illustrate our results.