Complexity bound of a Levenberg–Marquardt algorithm based on probabilistic Jacobian models

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED Optimization Letters Pub Date : 2024-07-18 DOI:10.1007/s11590-024-02140-x

Ruixue Zhao

引用次数: 0

Abstract

In this paper, we present a Levenberg–Marquardt algorithm for nonlinear equations, where the exact Jacobians are unavailable, but their model approximations can be built in some random fashion. We study the complexity of the algorithm and show that the upper bound of the iteration numbers in expectation to obtain a first order stationary point is \(O(\epsilon ^{-3})\).

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基于概率雅各布模型的 Levenberg-Marquardt 算法的复杂性约束

在本文中，我们提出了一种针对非线性方程的 Levenberg-Marquardt 算法，在这种非线性方程中，精确的 Jacobians 不可用，但其模型近似值可以通过某种随机方式建立。我们研究了该算法的复杂性，并证明获得一阶静止点的期望迭代次数上限为 \(O(\epsilon^{-3})\)。

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 Letters 管理科学-应用数学

CiteScore

3.40

自引率

6.20%

发文量

116

审稿时长

9 months

期刊介绍： Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published. Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field. Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.