{"title":"On computing sparse generalized inverses","authors":"Gabriel Ponte , Marcia Fampa , Jon Lee , Luze Xu","doi":"10.1016/j.orl.2023.107058","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research Letters","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167637723001992","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
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.
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.
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