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

Author

Listed:
  • Luis Rodríguez-Marín

    (E.T.S.I.I. Universidad Nacional de Educación a Distancia)

  • Miguel Sama

    (E.T.S.I.I. Universidad Nacional de Educación a Distancia)

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.

Suggested Citation

  • Luis Rodríguez-Marín & Miguel Sama, 2013. "Scalar Lagrange Multiplier Rules for Set-Valued Problems in Infinite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 683-700, March.
    • Handle: RePEc:spr:joptap:v:156:y:2013:i:3:d:10.1007_s10957-012-0154-y
    DOI: 10.1007/s10957-012-0154-y
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    References listed on IDEAS

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    1. M. Chinaie & J. Zafarani, 2009. "Image Space Analysis and Scalarization of Multivalued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 451-467, September.
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    3. P. Q. Khanh & N. D. Tuan, 2007. "Optimality Conditions for Nonsmooth Multiobjective Optimization Using Hadamard Directional Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 341-357, June.
    4. Joydeep Dutta & Christiane Tammer, 2006. "Lagrangian conditions for vector optimization in Banach spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 521-540, December.
    5. Johannes Jahn & Rüdiger Rauh, 1997. "Contingent epiderivatives and set-valued optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 193-211, June.
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