On computing sparse generalized inverses

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Letters Pub Date : 2023-12-15 DOI:10.1016/j.orl.2023.107058

Gabriel Ponte , Marcia Fampa , Jon Lee , Luze Xu

引用次数: 0

Abstract

The M-P (Moore-Penrose) pseudoinverse is used in several linear-algebra applications. It is convenient to construct sparse block-structured matrices satisfying some relevant properties of the M-P pseudoinverse for specific applications. Aiming at row-sparse generalized inverses, we consider 2,1-norm minimization (and generalizations). We show that a 2,1-norm minimizing generalized inverse satisfies two additional M-P properties, including one needed for computing least-squares solutions. We present formulations related to finding row-sparse generalized inverses that can be solved very efficiently, which we verify numerically.

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关于计算稀疏广义倒数

M-P（摩尔-彭罗斯）伪逆用于若干线性代数应用中。在特定应用中，构建满足 M-P 伪逆的某些相关性质的稀疏块结构矩阵非常方便。针对行稀疏广义逆，我们考虑了 2,1-norm 最小化（和广义）。我们证明，2,1-规范最小化广义逆满足两个额外的 M-P 特性，包括计算最小二乘法解所需的一个特性。我们提出了与寻找行稀疏广义逆相关的公式，这些公式可以非常高效地求解，我们也对其进行了数值验证。

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

Operations Research Letters 管理科学-运筹学与管理科学

CiteScore

2.10

自引率

9.10%

发文量

111

审稿时长

83 days

期刊介绍： Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.