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Lagrangian conditions for vector optimization in Banach spaces

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Abstract

We consider vector optimization problems on Banach spaces without convexity assumptions. Under the assumption that the objective function is locally Lipschitz we derive Lagrangian necessary conditions on the basis of Mordukhovich subdifferential and the approximate subdifferential by Ioffe using a non-convex scalarization scheme. Finally, we apply the results for deriving necessary conditions for weakly efficient solutions of non-convex location problems.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Kanpur, Kanpur, 208016, India

    Joydeep Dutta

  2. Fachbereich Mathematik und Informatik, Institut für Optimierung und Stochastik, Martin-Luther-Universität Halle-Wittenberg, 06099, Halle (Saale), Germany

    Christiane Tammer

Authors
  1. Joydeep Dutta
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  2. Christiane Tammer
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Correspondence to Christiane Tammer.

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Dutta, J., Tammer, C. Lagrangian conditions for vector optimization in Banach spaces. Math Meth Oper Res 64, 521–540 (2006). https://doi.org/10.1007/s00186-006-0079-z

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  • DOI: https://doi.org/10.1007/s00186-006-0079-z

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