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arXiv · 2305.17612

Fenchel Conjugate of Set-Valued Mappings

Nguyen Mau Nam·Gary Sandine·Nguyen Nang Thieu·Nguyen Dong Yen
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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 the 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.

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Nguyen Mau Nam, Gary Sandine, Nguyen Nang Thieu, Nguyen Dong Yen. 2023-05-28. Fenchel Conjugate of Set-Valued Mappings. https://arxiv.org/abs/2305.17612

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