Convergence rate of primal dual reciprocal Barrier Newton interior-point methods

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 1998-01-01 DOI:10.1080/10556789808805685

A. El-Bakry

引用次数: 0

Abstract

Primal-dual interior-point methods for linear programming are often motivated by a certaijn nonlinear transformation of the Karush-Kuhn-Tucker conditions of the logarithmic Barrier formulation. Recently, Nassar [5] studied the reciprocal Barrier function formulation of the problem. Using a similar nonlinear transformation, he proved local convergence fir Newton interior-point method on the resulting perturbed Karush-Kuhn-Tucker systerp. This result poses the question whether this method can exhibit fast convergence ral[e for linear programming. In this paper we prove that, for linear programming, Newton's method on the reciprocal Barrier formulation exhibits at best Q-linear convergence rattf. Moreover, an exact Q1 factor is established which precludes fast linear convergence

查看原文本刊更多论文

原始对偶互易势垒牛顿内点法的收敛速度

线性规划的原对偶内点法通常是由对数Barrier公式的Karush-Kuhn-Tucker条件的某种非线性变换所驱动的。最近，Nassar[5]研究了互易势垒函数的表述问题。利用类似的非线性变换，证明了牛顿内点法对扰动Karush-Kuhn-Tucker系统的局部收敛性。这一结果提出了该方法对于线性规划是否具有快速收敛性的问题。本文证明了对于线性规划，牛顿方法在互反Barrier公式上最优表现为q -线性收敛。此外，建立了一个精确的Q1因子，排除了快速线性收敛

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.