Unified Robust Necessary Optimality Conditions for Nonconvex Nonsmooth Uncertain Multiobjective Optimization

This paper is concerned with nonconvex nonsmooth uncertain multiobjective optimization problems, in which the decision variable of both objective and constraint functions is defined on Banach space while uncertain parameters are defined on arbitrary nonempty (may not be compact) sets. We employ the Stone-Cech compactification of uncertainty sets and the upper semicontinuous regularization of original functions with respect to uncertain parameters, giving rise to unified robust necessary optimality conditions for the local robust weakly efficient solution of the considered problem. Moreover, we derive weak and strong KKT robust necessary conditions via the constraint qualification and the regularity condition, respectively. Several examples are provided to illustrate the validity of our results.

Automated summary

This paper investigates nonconvex nonsmooth uncertain multiobjective optimization problems, where the decision variable is defined on a Banach space and uncertain parameters are defined on arbitrary nonempty sets. The Stone-Cech compactification of uncertainty sets and the upper semicontinuous regularization of original functions are employed to derive robust necessary optimality conditions for the local robust weakly efficient solution. Weak and strong KKT robust necessary conditions are also obtained based on the constraint qualification and the regularity condition. Several examples are provided to demonstrate the validity of the results.