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On generalized-convex constrained multi-objective optimization

Christian GŁnther (Christian.Guenther***at***mathematik.uni-halle.de)
Christiane Tammer (Christiane.Tammer***at***mathematik.uni-halle.de)

Abstract: 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.

Keywords: Multi-objective optimization, Pareto efficiency, Generalized convexity, Constrained optimization, Convex and nonconvex constraints, Slater constraint qualification

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: C. GŁnther 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)

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Entry Submitted: 04/01/2017
Entry Accepted: 04/01/2017
Entry Last Modified: 08/25/2019

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