正则对称不定系统的线性和二次优化的内点法

IF 1.4 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Optimization Methods & Software Pub Date : 1999-01-01 DOI:10.1080/10556789908805754

A. Altman, J. Gondzio

{"title":"正则对称不定系统的线性和二次优化的内点法","authors":"A. Altman, J. Gondzio","doi":"10.1080/10556789908805754","DOIUrl":null,"url":null,"abstract":"This paper presents linear algebra techniques used in the implementation of an interior point method for solving linear programs and convex quadratic programs with linear constraint. The new regularization techniques for Newton equation system applicable to both symmetric positive definite and symmetric indefinite systems are described. They transform the latter to quasidefinite systems known to be strongly factorizable to a form of Cholesky-like factorization.","PeriodicalId":54673,"journal":{"name":"Optimization Methods & Software","volume":"18 1","pages":"275-302"},"PeriodicalIF":1.4000,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"178","resultStr":"{\"title\":\"Regularized Symmetric Indefinite Systems in Interior Point Methods for Linear and Quadratic Optimization\",\"authors\":\"A. Altman, J. Gondzio\",\"doi\":\"10.1080/10556789908805754\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents linear algebra techniques used in the implementation of an interior point method for solving linear programs and convex quadratic programs with linear constraint. The new regularization techniques for Newton equation system applicable to both symmetric positive definite and symmetric indefinite systems are described. They transform the latter to quasidefinite systems known to be strongly factorizable to a form of Cholesky-like factorization.\",\"PeriodicalId\":54673,\"journal\":{\"name\":\"Optimization Methods & Software\",\"volume\":\"18 1\",\"pages\":\"275-302\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"1999-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"178\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Optimization Methods & Software\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1080/10556789908805754\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, SOFTWARE ENGINEERING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optimization Methods & Software","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1080/10556789908805754","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}

引用次数: 178

摘要

本文介绍了求解线性规划和带线性约束的凸二次规划的内点法的线性代数技术。描述了牛顿方程组的正则化新技术，该技术适用于对称正定系统和对称不定系统。它们将后者转化为准定系统，这些准定系统是强可因式分解的一种形式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Regularized Symmetric Indefinite Systems in Interior Point Methods for Linear and Quadratic Optimization

This paper presents linear algebra techniques used in the implementation of an interior point method for solving linear programs and convex quadratic programs with linear constraint. The new regularization techniques for Newton equation system applicable to both symmetric positive definite and symmetric indefinite systems are described. They transform the latter to quasidefinite systems known to be strongly factorizable to a form of Cholesky-like factorization.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Optimization Methods & Software 工程技术-计算机：软件工程

CiteScore

4.50

自引率

0.00%

发文量

审稿时长

7 months

期刊介绍： Optimization Methods and Software publishes refereed papers on the latest developments in the theory and realization of optimization methods, with particular emphasis on the interface between software development and algorithm design. Topics include: Theory, implementation and performance evaluation of algorithms and computer codes for linear, nonlinear, discrete, stochastic optimization and optimal control. This includes in particular conic, semi-definite, mixed integer, network, non-smooth, multi-objective and global optimization by deterministic or nondeterministic algorithms. Algorithms and software for complementarity, variational inequalities and equilibrium problems, and also for solving inverse problems, systems of nonlinear equations and the numerical study of parameter dependent operators. Various aspects of efficient and user-friendly implementations: e.g. automatic differentiation, massively parallel optimization, distributed computing, on-line algorithms, error sensitivity and validity analysis, problem scaling, stopping criteria and symbolic numeric interfaces. Theoretical studies with clear potential for applications and successful applications of specially adapted optimization methods and software to fields like engineering, machine learning, data mining, economics, finance, biology, or medicine. These submissions should not consist solely of the straightforward use of standard optimization techniques.