A Notion of Fenchel Conjugate for Set-Valued Mappings

Published In

Journal of Optimization Theory and Applications

Document Type

Citation

Publication Date

5-28-2024

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.

Rights

© 2024 Springer Nature

DOI

10.1007/s10957-024-02455-w

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