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On the Fritz John saddle point problem for differentiable multiobjective optimization

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Abstract

In this contribution, the relationship between saddle points of Lagrangian functions associated with the inequality constrained multiobjective optimization problem and Fritz John critical points are presented under generalized notions of convexity. Assuming invexity and an extended Slater-type condition upon the multiobjective problem, a regular solution to the Fritz-John system is obtained that encompasses all the objective functions. Also, a new class of generalized convex problems is defined, and its connections with other existing classes are established.

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Acknowledgments

The authors are grateful to the anonymous reviewers, whose comments improved the presentation of the manuscript. This work was partially supported by the grants UNS 24/L082, E097/13, CNPq 304032/2010-7, FAPESP 2013/05475-7 and 2013/07375-0.

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Authors and Affiliations

  1. Universidad Nacional del Sur, Buenos Aires, Argentina

    Maria C. Maciel

  2. Universidade Estadual de Campinas, Campinas, SP, Brazil

    Sandra A. Santos

  3. Universidad Nacional del Comahue (AR), Neuquén, Argentina

    Graciela N. Sottosanto

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  1. Maria C. Maciel
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  2. Sandra A. Santos
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  3. Graciela N. Sottosanto
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Correspondence to Sandra A. Santos.

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Maciel, M.C., Santos, S.A. & Sottosanto, G.N. On the Fritz John saddle point problem for differentiable multiobjective optimization. OPSEARCH 53, 917–933 (2016). https://doi.org/10.1007/s12597-016-0253-x

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