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

Christian Günther () and Christiane Tammer
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Christian Günther: Martin Luther University Halle-Wittenberg
Christiane Tammer: Martin Luther University Halle-Wittenberg

Mathematical Methods of Operations Research, 2016, vol. 84, issue 2, No 5, 359-387

Abstract: 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 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00186-016-0547-z

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