Two inertial proximal coordinate algorithms for a family of nonsmooth and nonconvex optimization problems

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2024-11-22 DOI:10.1016/j.automatica.2024.111992

Ya Zheng Dang , Jie Sun , Kok Lay Teo

引用次数: 0

Abstract

The inertial proximal method is extended to minimize the sum of a series of separable nonconvex and possibly nonsmooth objective functions and a smooth nonseparable function (possibly nonconvex). Here, we propose two new algorithms. The first one is an inertial proximal coordinate subgradient algorithm, which updates the variables by employing the proximal subgradients of each separable function at the current point. The second one is an inertial proximal block coordinate method, which updates the variables by using the subgradients of the separable functions at the partially updated points. Global convergence is guaranteed under the Kurdyka–Łojasiewicz (KŁ) property and some additional mild assumptions. Convergence rate is derived based on the Łojasiewicz exponent. Two numerical examples are given to illustrate the effectiveness of the algorithms.

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针对一系列非光滑和非凸优化问题的两种惯性近坐标算法

惯性近似法被扩展用于最小化一系列可分离的非凸、可能是非光滑目标函数和一个光滑的不可分离函数（可能是非凸）之和。在此，我们提出了两种新算法。第一种是惯性近坐标子梯度算法，它通过使用每个可分离函数在当前点的近坐标子梯度来更新变量。第二种是惯性近似块坐标法，通过使用部分更新点的可分离函数子梯度来更新变量。在 Kurdyka-Łojasiewicz (KŁ) 属性和一些额外的温和假设下，保证了全局收敛。收敛率是根据 Łojasiewicz 指数推导出来的。给出了两个数值示例来说明算法的有效性。

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

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.