In this paper, we consider multi-objective optimization problems involving not necessarily convex constraints and componentwise generalized-convex (e.g., semi-strictly quasi-convex, quasi-convex, or explicitly quasi-convex) vector-valued objective functions that are acting between a real linear topological pre-image space and a finite dimensional image space. For these multi-objective optimization problems, we show that the set of (strictly, weakly) efficient solutions can be computed completely by using at most two corresponding multi-objective optimization problems with a new feasible set that is a convex upper set of the original feasible set. Our approach relies on the fact that the original feasible set can be described using level sets of a certain real-valued function (a kind of penalization function). Finally, we apply our approach to problems where the constraints are given by a system of inequalities with a finite number of constraint functions.
Citation
C. Günther and C. Tammer, On generalized-convex constrained multi-objective optimization, Pure and Applied Functional Analysis, Volume 3, Number 3, Pages 429-461, 2018 (see http://www.ybook.co.jp/online2/oppafa/vol3/p429.html)