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Lagrange Multipliers in Convex Set Optimization with the Set and Vector Criteria

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Abstract

In the setting of normed spaces ordered by a convex cone, we define a set-valued optimization problem where the feasible set is given by a cone-constraint and we derive Lagrange optimality conditions for weakly efficient solutions of the problem following both the set and the vector solution criterion. For the set criterion, a lower set less preorder is considered. The optimality conditions are expressed in terms of coderivatives and are obtained through scalarization, by using a nonlinear scalarizing functional based on the oriented distance.

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Acknowledgements

The authors are grateful to the anonymous referees for their useful suggestions and remarks.

This work was partially supported by the 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. Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia (UNED), calle Juan del Rosal, 12, 28040, Madrid, Spain

    L. Huerga, B. Jiménez & V. Novo

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  1. L. Huerga
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  2. B. Jiménez
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  3. V. Novo
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Correspondence to V. Novo.

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Dedicated to Marco A. López on the occasion of his 70th birthday.

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Huerga, L., Jiménez, B. & Novo, V. Lagrange Multipliers in Convex Set Optimization with the Set and Vector Criteria. Vietnam J. Math. 48, 345–362 (2020). https://doi.org/10.1007/s10013-020-00404-4

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  • DOI: https://doi.org/10.1007/s10013-020-00404-4

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