针对$$p \ge 2$$的$$ell _{p}$$-norm圆锥优化问题的增强拉格朗日法的收敛性分析

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-06 DOI:10.1007/s11075-024-01912-x

Benqi Liu, Kai Gong, Liwei Zhang

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引用次数: 0

摘要

本文主要研究了针对 $\varvec\{ell }_\varvec{p}}-orm cone 优化问题的增强拉格朗日法（ALM）的收敛性分析。我们研究了增强拉格朗日函数和（\varvec{ell }_{\varvec{p}}）-规范锥的一些特性。此外，在雅各布唯一性条件下，我们证明了 ALM 在求解 \(\varvec{ell }_{varvec{p}}$-norm cone 优化问题时的局部收敛率与 $\varvec{p} \varvec{ge } \varvec{2}$ 成正比、其中，惩罚参数 $\varvec{r}$不小于阈值 $\varvec\{hat{r}}$。在数值模拟中，我们成功验证了 ALM 的有效性和收敛性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$Convergence analysis of the augmented Lagrangian method for $$\ell _{p}$$ -norm cone optimization problems with $$p \ge 2$$$

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Convergence analysis of the augmented Lagrangian method for $$\ell _{p}$$ -norm cone optimization problems with $$p \ge 2$$

This paper focuses on the convergence analysis of the augmented Lagrangian method (ALM) for $\varvec{\ell }_{\varvec{p}}$-norm cone optimization problems. We investigate some properties of the augmented Lagrangian function and $\varvec{\ell }_{\varvec{p}}$-norm cone. Moreover, under the Jacobian uniqueness conditions, we prove that the local convergence rate of ALM for solving $\varvec{\ell }_{\varvec{p}}$-norm cone optimization problems with $\varvec{p} \varvec{\ge } \varvec{2}$ is proportional to $\varvec{1}\varvec{/}\varvec{r}$, where the penalty parameter $\varvec{r}$ is not less than a threshold $\varvec{\hat{r}}$. In numerical simulations, we successfully validate the effectiveness and convergence properties of ALM.

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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.