SPIRAL: a superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-29 DOI:10.1007/s10589-023-00550-8

Pourya Behmandpoor, Puya Latafat, Andreas Themelis, Marc Moonen, Panagiotis Patrinos

引用次数: 0

Abstract

We introduce SPIRAL, a SuPerlinearly convergent Incremental pRoximal ALgorithm, for solving nonconvex regularized finite sum problems under a relative smoothness assumption. Each iteration of SPIRAL consists of an inner and an outer loop. It combines incremental gradient updates with a linesearch that has the remarkable property of never being triggered asymptotically, leading to superlinear convergence under mild assumptions at the limit point. Simulation results with L-BFGS directions on different convex, nonconvex, and non-Lipschitz differentiable problems show that our algorithm, as well as its adaptive variant, are competitive to the state of the art.

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SPIRAL：非凸有限和最小化的超线性收敛增量近端算法

我们介绍了 SPIRAL，这是一种线性收敛的增量最小算法，用于求解相对平滑假设下的非凸正则化有限和问题。SPIRAL 的每次迭代都由一个内循环和一个外循环组成。它将增量梯度更新与线性搜索相结合，线性搜索具有从不触发渐近的显著特性，从而在极限点的温和假设下实现超线性收敛。在不同的凸性、非凸性和非 Lipschitz 可微分问题上使用 L-BFGS 方向的模拟结果表明，我们的算法及其自适应变体与现有技术相比具有竞争力。

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

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.