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

Author

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  • Christian Günther

    (Martin Luther University Halle-Wittenberg)

  • Christiane Tammer

    (Martin Luther University Halle-Wittenberg)

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.

Suggested Citation

  • Christian Günther & Christiane Tammer, 2016. "Relationships between constrained and unconstrained multi-objective optimization and application in location theory," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(2), pages 359-387, October.
    • Handle: RePEc:spr:mathme:v:84:y:2016:i:2:d:10.1007_s00186-016-0547-z
    DOI: 10.1007/s00186-016-0547-z
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    References listed on IDEAS

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    1. J.-F. Thisse & J. E. Ward & R. E. Wendell, 1984. "Some Properties of Location Problems with Block and Round Norms," Operations Research, INFORMS, vol. 32(6), pages 1309-1327, December.
    2. Alberto Cambini & Laura Martein, 2009. "Generalized Convexity and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-70876-6, December.
    3. A.M. Rodríguez-Chía & J. Puerto, 2002. "Geometrical Description of the Weakly Efficient Solution Set for Multicriteria Location Problems," Annals of Operations Research, Springer, vol. 111(1), pages 181-196, March.
    4. Ndiaye, M. & Michelot, C., 1998. "Efficiency in constrained continuous location," European Journal of Operational Research, Elsevier, vol. 104(2), pages 288-298, January.
    5. Stefan Nickel & Justo Puerto & Antonio M. Rodríguez-Chía, 2015. "Location Problems with Multiple Criteria," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 205-247, Springer.
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    Cited by:

    1. Gabriele Eichfelder & Kathrin Klamroth & Julia Niebling, 2021. "Nonconvex constrained optimization by a filtering branch and bound," Journal of Global Optimization, Springer, vol. 80(1), pages 31-61, May.
    2. Marius Durea & Radu Strugariu & Christiane Tammer, 2017. "On Some Methods to Derive Necessary and Sufficient Optimality Conditions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 738-763, December.

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