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

IF 1.4 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Optimization Methods & Software 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

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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。

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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.