On Roughly Convex Multiobjective Optimization

In this paper, we consider a roughly convex multiobjective optimization problem and use the concept of the outer γ -convexity (resp., the γ -convexlikeness) of the objective mapping, where γ >0 is the roughness degree of the objective one, to show that every γ -local weak efficient solution (resp., γ -local efficient solution) of the considered problem is also a global weak efficient one (resp., global efficient one). Necessary and sufficient conditions for efficiency solutions are established by using γ -subdifferentials. Examples are also given to illustrate the obtained results.