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Relationships between constrained and unconstrained multi-objective optimization and application in location theory

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

Abstract: This article deals with constrained multi-objective optimization problems. The main purpose of the article is to investigate relationships between constrained and unconstrained multi-objective optimization problems. Under suitable assumptions (e.g., generalized convexity assumptions) we derive a characterization of the set of (strictly, weakly) efficient solutions of a constrained multi-objective optimization problem using characterizations of the sets of (strictly, weakly) efficient solutions of unconstrained multi-objective optimization problems. We demonstrate the usefulness of the results by applying it on constrained multi-objective location problems. Using our new results we show that special classes of constrained multi-objective location problems (e.g., point-objective location problems, Weber location problems, center location problems) can be completely solved with the help of algorithms for the unconstrained case.

Keywords: multi-objective optimization; Pareto efficiency; constrained optimization; unconstrained optimization; generalized convexity; location theory; gauges

Category 1: Other Topics (Multi-Criteria Optimization )

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

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Mathematical Methods of Operations Research, DOI: 10.1007/s00186-016-0547-z , 2016


Entry Submitted: 11/04/2015
Entry Accepted: 11/12/2015
Entry Last Modified: 01/11/2018

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