线性优化的改进迭代界多项式内点算法

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED

Japan Journal of Industrial and Applied Mathematics Pub Date : 2023-12-01 DOI:10.1007/s13160-023-00630-6

Liying Liu, Tao Hua

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引用次数: 0

摘要

本文提出了一种基于修正对数屏障核函数的多项式原对偶内点线性优化算法。推导了大更新内点法和小更新内点法的迭代边界。结果表明，大更新内点法与小更新内点法具有相同的多项式复杂度，这是已知的迭代界。我们的结果填补了大更新内点法和小更新内点法在理论复杂度界上长期存在的空白。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A polynomial interior-point algorithm with improved iteration bounds for linear optimization

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A polynomial interior-point algorithm with improved iteration bounds for linear optimization

In this paper, we present a polynomial primal-dual interior-point algorithm for linear optimization based on a modified logarithmic barrier kernel function. Iteration bounds for the large-update interior-point method and the small-update interior-point method are derived. It is shown that the large-update interior-point method has the same polynomial complexity as the small-update interior-point method, which is the best known iteration bounds. Our result closes a long-existing gap in the theoretical complexity bounds for large-update interior-point method and small-update interior-point method.

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来源期刊

Japan Journal of Industrial and Applied Mathematics 数学-应用数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Japan Journal of Industrial and Applied Mathematics (JJIAM) is intended to provide an international forum for the expression of new ideas, as well as a site for the presentation of original research in various fields of the mathematical sciences. Consequently the most welcome types of articles are those which provide new insights into and methods for mathematical structures of various phenomena in the natural, social and industrial sciences, those which link real-world phenomena and mathematics through modeling and analysis, and those which impact the development of the mathematical sciences. The scope of the journal covers applied mathematical analysis, computational techniques and industrial mathematics.