定值映射的芬切尔共轭概念

IF 1.6 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Optimization Theory and Applications Pub Date : 2024-05-28 DOI:10.1007/s10957-024-02455-w

Nguyen Mau Nam, Gary Sandine, Nguyen Nang Thieu, Nguyen Dong Yen

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引用次数: 0

摘要

在本文中，我们提出了一个新颖的概念，即定值映射的芬切尔共轭，并研究了它在有限维度和无限维度中的性质。在确定了定值映射的 Fenchel 共轭的一些基本性质后，我们推导出了它在各种情况下的主要微积分规则。我们的方法是几何方法，并从 B.S. Mordukhovich 及其合作者在变分和凸分析中成功应用该方法中获得灵感。随后，我们证明了我们对定值映射的芬切尔共轭的新发现可以用来获得有限维度和无限维度凸泛微分的许多新旧微积分规则。

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A Notion of Fenchel Conjugate for Set-Valued Mappings

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.

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来源期刊

Journal of Optimization Theory and Applications 数学-应用数学

CiteScore

3.30

自引率

5.30%

发文量

149

审稿时长

9.9 months

期刊介绍： The Journal of Optimization Theory and Applications is devoted to the publication of carefully selected regular papers, invited papers, survey papers, technical notes, book notices, and forums that cover mathematical optimization techniques and their applications to science and engineering. Typical theoretical areas include linear, nonlinear, mathematical, and dynamic programming. Among the areas of application covered are mathematical economics, mathematical physics and biology, and aerospace, chemical, civil, electrical, and mechanical engineering.