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On second-order Fritz John type optimality conditions in nonsmooth multiobjective programming

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Abstract

We study a multiobjective optimization program with a feasible set defined by equality constraints and a generalized inequality constraint. We suppose that the functions involved are Fréchet differentiable and their Fréchet derivatives are continuous or stable at the point considered. We provide necessary second order optimality conditions and also sufficient conditions via a Fritz John type Lagrange multiplier rule and a set-valued second order directional derivative, in such a way that our sufficient conditions are close to the necessary conditions. Some consequences are obtained for parabolic directionally differentiable functions and C 1,1 functions, in this last case, expressed by means of the second order Clarke subdifferential. Some illustrative examples are also given.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, E.T.S.I. Informática, Edificio de Tecnologías de la Información y las Telecomunicaciones, Universidad de Valladolid, Campus Miguel Delibes, s/n, 47011, Valladolid, Spain

    C. Gutiérrez

  2. Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia, Calle Juan del Rosal 12, 28040, Madrid, Spain

    B. Jiménez & V. Novo

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  1. C. Gutiérrez
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  2. B. Jiménez
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  3. V. Novo
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Correspondence to B. Jiménez.

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Gutiérrez, C., Jiménez, B. & Novo, V. On second-order Fritz John type optimality conditions in nonsmooth multiobjective programming. Math. Program. 123, 199–223 (2010). https://doi.org/10.1007/s10107-009-0318-1

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  • DOI: https://doi.org/10.1007/s10107-009-0318-1

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