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A Notion of Fenchel Conjugate for Set-Valued Mappings

Author

Listed:
  • Nguyen Mau Nam

    (Portland State University)

  • Gary Sandine

    (Portland State University)

  • Nguyen Nang Thieu

    (Vietnam Academy of Science and Technology)

  • Nguyen Dong Yen

    (Vietnam Academy of Science and Technology)

Abstract

In this paper, we present a novel concept of the Fenchel conjugate for set-valued mappings and investigate its properties in finite and infinite dimensions. After establishing some fundamental properties of the Fenchel conjugate for set-valued mappings, we derive its main calculus rules in various settings. Our approach is geometric and draws inspiration from the successful application of this method by B.S. Mordukhovich and coauthors in variational and convex analysis. Subsequently, we demonstrate that our new findings for the Fenchel conjugate of set-valued mappings can be utilized to obtain many old and new calculus rules of convex generalized differentiation in both finite and infinite dimensions.

Suggested Citation

  • Nguyen Mau Nam & Gary Sandine & Nguyen Nang Thieu & Nguyen Dong Yen, 2024. "A Notion of Fenchel Conjugate for Set-Valued Mappings," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1263-1292, November.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:2:d:10.1007_s10957-024-02455-w
    DOI: 10.1007/s10957-024-02455-w
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    References listed on IDEAS

    as
    1. Wen Song, 1998. "A generalization of Fenchel duality in set-valued vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 259-272, November.
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