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Duality related to approximate proper solutions of vector optimization problems

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Abstract

In this work we introduce two approximate duality approaches for vector optimization problems. The first one by means of approximate solutions of a scalar Lagrangian, and the second one by considering \((C,\varepsilon )\)-proper efficient solutions of a recently introduced set-valued vector Lagrangian. In both approaches we obtain weak and strong duality results for \((C,\varepsilon )\)-proper efficient solutions of the primal problem, under generalized convexity assumptions. Due to the suitable limit behaviour of the \((C,\varepsilon )\)-proper efficient solutions when the error \(\varepsilon \) tends to zero, the obtained duality results extend and improve several others in the literature.

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Acknowledgments

This work was partially supported by Ministerio de Economía y Competitividad (Spain) under project MTM2012-30942. The authors are very grateful to the anonymous referees for their helpful comments and suggestions.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, E.T.S. de Ingenieros de Telecomunicación, Universidad de Valladolid, Paseo de Belén 15, Campus Miguel Delibes, 47011, Valladolid, Spain

    C. Gutiérrez

  2. Departamento de Matemática Aplicada, E.T.S.I. Industriales, UNED, c/ Juan del Rosal 12, Ciudad Universitaria, 28040, Madrid, Spain

    L. Huerga & V. Novo

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

    C. Tammer

Authors
  1. C. Gutiérrez
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  2. L. Huerga
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  3. V. Novo
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  4. C. Tammer
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Corresponding author

Correspondence to V. Novo.

Additional information

L. Huerga: Researcher of Spanish FPI Fellowship Programme (BES-2010-033742).

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Gutiérrez, C., Huerga, L., Novo, V. et al. Duality related to approximate proper solutions of vector optimization problems. J Glob Optim 64, 117–139 (2016). https://doi.org/10.1007/s10898-015-0366-4

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  • DOI: https://doi.org/10.1007/s10898-015-0366-4

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