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Optimality conditions for approximate proper solutions in multiobjective optimization with polyhedral cones

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Abstract

In this paper, we provide optimality conditions for approximate proper solutions of a multiobjective optimization problem, whose feasible set is given by a cone constraint and the ordering cone is polyhedral. A first class of optimality conditions is given by means of a nonlinear scalar Lagrangian and the second kind through a linear scalarization technique, under generalized convexity hypotheses, that lets us derive a Kuhn–Tucker multiplier rule.

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Acknowledgements

The authors are very grateful to the anonymous referees for their careful reading and their helpful comments and suggestions. This work was partially supported by Ministerio de Ciencia, Innovación y Universidades (MCIU), Agencia Estatal de Investigación (AEI) (Spain) and Fondo Europeo de Desarrollo Regional (FEDER) under Project PGC2018-096899-B-I00 (MCIU/AEI/FEDER, UE).

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Authors and Affiliations

  1. IMUVA (Institute of Mathematics of University of Valladolid), Paseo de Belén S/N, Campus Miguel Delibes, 47011, Valladolid, Spain

    C. Gutiérrez

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

    L. Huerga, B. Jiménez & V. Novo

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  1. C. Gutiérrez
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  2. L. Huerga
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  4. V. Novo
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Correspondence to V. Novo.

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Gutiérrez, C., Huerga, L., Jiménez, B. et al. Optimality conditions for approximate proper solutions in multiobjective optimization with polyhedral cones. TOP 28, 526–544 (2020). https://doi.org/10.1007/s11750-020-00546-1

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