ABSTRACT
In this chapter, we deal with penalization approaches in multi-objective optimization that aim to replace the original constrained optimization problem (with not necessarily convex feasible set) by some related problems with an easier structured feasible set (or actually by some unconstrained problems). We focus on the application of the vectorial penalization approach to constrained multi-objective optimization problems with objective functions that are acting between a normed pre-image space and an image space given by a finite-dimensional Euclidean space. For deriving some main results, we use certain generalized convexity notions that are appropriate for such a class of vector-valued functions (e.g., component wise semi-strict quasi-convexity and component wise quasi-convexity). In our study, we concentrate on both local as well as global Pareto efficient solutions. At the end, for specific problems with functional inequality constraints, we gain some new insights in the topic of vectorial penalization by considering appropriate constraint qualifications (such as Slater’s condition, Mangasarian-Fromowitz condition, and Lassere’s non-degeneracy condition).
