Mixed lattice structures and cone projections

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Optimization Letters Pub Date : 2023-12-02 DOI:10.1007/s11590-023-02075-9

Jani Jokela

引用次数: 1

Abstract

Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems, various unifying ideas have been introduced, including asymmetric vector-valued norms and certain generalized lattice-like operations. We propose a new perspective on these studies by describing how the problem of cone projection can be formulated using an order-theoretic formalism developed in this paper. The underlying mathematical structure is a partially ordered vector space that generalizes the notion of a vector lattice by using two partial orderings and having certain lattice-type properties with respect to these orderings. In this note we introduce a generalization of these so-called mixed lattice spaces, and we show how such structures arise quite naturally in some of the applications mentioned above.

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混合晶格结构和圆锥投影

闭凸锥投影问题是优化理论及相关领域中经常遇到的问题。为了研究这些问题，引入了各种统一思想，包括不对称向量值范数和某些广义类格运算。我们提出了一个新的研究视角，描述了如何利用本文发展的有序理论形式来表述锥投影问题。其基本的数学结构是一个偏序向量空间，它通过使用两个偏序和关于这些序的某些格型性质来推广向量晶格的概念。在这篇笔记中，我们介绍了这些所谓的混合晶格空间的推广，并展示了这些结构是如何在上面提到的一些应用中自然出现的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.