A Notion of Fenchel Conjugate for Set-Valued Mappings

被引：1

作者：

Nam, Nguyen Mau ^{[1
]}

Sandine, Gary ^{[1
]}

Thieu, Nguyen Nang ^{[2
]}

Yen, Nguyen Dong ^{[2
]}

机构：

[1] Portland State Univ, Fariborz Maseeh Dept Math & Stat, Portland, OR 97207 USA

[2] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet, Hanoi 10307, Vietnam

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2024年 / 203卷 / 02期

基金：

美国国家科学基金会;

关键词：

Fenchel conjugate; Coderivative; Subdifferential; Convex set-valued mapping; Relative interior; Quasi-relative interior; Strong quasi-relative interior; DUALITY;

D O I：

10.1007/s10957-024-02455-w

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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.

引用

页码：1263 / 1292

页数：30

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