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Some Variants of the Ekeland Variational Principle for a Set-Valued Map

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  • T. X. D. Ha

    (Hanoi Institute of Mathematics)

Abstract

This paper deals with the Ekeland variational principle (EVP) for a set-valued map F with values in a vector space E. Using the concept of cone extension and the Mordukhovich coderivative, we formulate some variants of the EVP for F under various continuity assumptions. We investigate also the stability of a set-valued EVP. Our approach is motivated by the set approach proposed by Kuroiwa for minimizing set-valued maps.

Suggested Citation

  • T. X. D. Ha, 2005. "Some Variants of the Ekeland Variational Principle for a Set-Valued Map," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 187-206, January.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:1:d:10.1007_s10957-004-6472-y
    DOI: 10.1007/s10957-004-6472-y
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    References listed on IDEAS

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    1. Hedy Attouch & Hassan Riahi, 1993. "Stability Results for Ekeland's ε-Variational Principle and Cone Extremal Solutions," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 173-201, February.
    2. Guang Ya Chen & X. X. Huang, 1998. "Ekeland's ε-variational principle for set-valued mappings," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 181-186, November.
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