Dual and generalized dual cones in Banach spaces

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Optimization Letters Pub Date : 2024-06-11 DOI:10.1007/s11590-024-02126-9

Akhtar A. Khan, Dezhou Kong, Jinlu Li

引用次数: 0

Abstract

This paper proposes and analyzes the notion of dual cones associated with the metric projection and generalized projection in Banach spaces. We show that the dual cones, related to the metric projection and generalized metric projection, lose many important properties in transitioning from Hilbert spaces to Banach spaces. We also propose and analyze the notions of faces and visions in Banach spaces and relate them to metric projection and generalized projection. We provide many illustrative examples to give insight into the given results

查看原文本刊更多论文

巴拿赫空间中的对偶锥和广义对偶锥

本文提出并分析了与巴拿赫空间中的度量投影和广义投影相关的对偶锥概念。我们表明，与公投影和广义公投影相关的对偶锥在从希尔伯特空间过渡到巴拿赫空间时会失去许多重要性质。我们还提出并分析了巴拿赫空间中的面和视概念，并将它们与度量投影和广义投影联系起来。我们提供了许多说明性的例子，让大家深入了解所给出的结果

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Optimization Letters 管理科学-应用数学

CiteScore

3.40

自引率

6.20%

发文量

116

审稿时长

9 months

期刊介绍： Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published. Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field. Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.