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On Some Methods to Derive Necessary and Sufficient Optimality Conditions in Vector Optimization

Author

Listed:
  • Marius Durea

    (“Al. I. Cuza” University)

  • Radu Strugariu

    (“Gh. Asachi” Technical University)

  • Christiane Tammer

    (Martin-Luther-Universität Halle-Wittenberg)

Abstract

The aim of this paper is to address new approaches, in separate ways, to necessary and, respectively, sufficient optimality conditions in constrained vector optimization. In this respect, for the necessary optimality conditions that we derive, we use a kind of vectorial penalization technique, while for the sufficient optimality conditions we make use of an appropriate scalarization method. In both cases, the approaches couple a basic technique (of penalization or scalarization, respectively) with several results in variational analysis and optimization obtained by the authors in the last years. These combinations allow us to arrive to optimality conditions which are, in terms of assumptions made, new.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:175:y:2017:i:3:d:10.1007_s10957-016-1059-y
    DOI: 10.1007/s10957-016-1059-y
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    References listed on IDEAS

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    1. 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.
    2. Jean-Paul Penot, 1998. "Cooperative behavior of functions, relations and sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 229-246, November.
    3. M. Durea, 2010. "Remarks on strict efficiency in scalar and vector optimization," Journal of Global Optimization, Springer, vol. 47(1), pages 13-27, May.
    4. Marius Durea & Radu Strugariu & Christiane Tammer, 2015. "On set-valued optimization problems with variable ordering structure," Journal of Global Optimization, Springer, vol. 61(4), pages 745-767, April.
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