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

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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.

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Acknowledgments

The authors wish to thank the anonymous referees for their valuable comments.

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Authors and Affiliations

  1. Faculty of Natural Sciences II, Institute for Mathematics, Martin Luther University Halle-Wittenberg, 06099, Halle (Saale), Germany

    Christian Günther & Christiane Tammer

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  1. Christian Günther
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  2. Christiane Tammer
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Correspondence to Christian Günther.

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Günther, C., Tammer, C. Relationships between constrained and unconstrained multi-objective optimization and application in location theory. Math Meth Oper Res 84, 359–387 (2016). https://doi.org/10.1007/s00186-016-0547-z

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  • DOI: https://doi.org/10.1007/s00186-016-0547-z

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