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Scalar Lagrange Multiplier Rules for Set-Valued Problems in Infinite-Dimensional Spaces

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Abstract

This paper deals with Lagrange multiplier rules for constrained set-valued optimization problems in infinite-dimensional spaces, where the multipliers appear as scalarization functions of the maps instead of the derivatives. These rules provide necessary conditions for weak minimizers under hypotheses of stability, convexity, and directional compactness. Counterexamples show that the hypotheses are minimal.

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Acknowledgements

The work for the second author is partially supported by Ministerio de Ciencia (Spain), project MTM2009-09493.

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Authors and Affiliations

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

    Luis Rodríguez-Marín & Miguel Sama

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  1. Luis Rodríguez-Marín
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  2. Miguel Sama
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Correspondence to Miguel Sama.

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Communicated by Johannes Jahn.

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Rodríguez-Marín, L., Sama, M. Scalar Lagrange Multiplier Rules for Set-Valued Problems in Infinite-Dimensional Spaces. J Optim Theory Appl 156, 683–700 (2013). https://doi.org/10.1007/s10957-012-0154-y

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  • DOI: https://doi.org/10.1007/s10957-012-0154-y

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