一种加速的直流规划双近邻梯度算法

IF 1.1 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Asia-Pacific Journal of Operational Research Pub Date : 2023-11-04 DOI:10.1142/s0217595923500288

Gaoxi Li, Ying Yi, Yingquan Huang

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引用次数: 0

摘要

双近端梯度算法(DPGA)是对经典凸差分算法(DCA)的改进，用于求解凸差分优化问题。在本文中，我们提出了一种加速版本的双邻点梯度算法用于DC规划，其中目标函数由三个凸模块组成(其中只有一个模块是光滑的)。在目标函数满足Kurdyka -[公式:见文]ojasiewicz (K[公式:见文])性质的条件下，建立了算法生成序列的收敛性，并证明其收敛速度不弱于DPGA。在一个图像处理模型上进行的数值实验表明，与DPGA相比，ADPGA的迭代次数平均减少43.57%，运行时间平均减少43.47%。

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An accelerated double-proximal gradient algorithm for DC programming

The double-proximal gradient algorithm (DPGA) is a new variant of the classical difference-of-convex algorithm (DCA) for solving difference-of-convex (DC) optimization problems. In this paper, we propose an accelerated version of the double-proximal gradient algorithm for DC programming, in which the objective function consists of three convex modules (only one module is smooth). We establish convergence of the sequence generated by our algorithm if the objective function satisfies the Kurdyka–[Formula: see text]ojasiewicz (K[Formula: see text]) property and show that its convergence rate is not weaker than DPGA. Compared with DPGA, the numerical experiments on an image processing model show that the number of iterations of ADPGA is reduced by 43.57% and the running time is reduced by 43.47% on average.

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来源期刊

Asia-Pacific Journal of Operational Research 管理科学-运筹学与管理科学

CiteScore

2.00

自引率

14.30%

发文量

审稿时长

14.2 months

期刊介绍： The Asia-Pacific Journal of Operational Research (APJOR) provides a forum for practitioners, academics and researchers in Operational Research and related fields, within and beyond the Asia-Pacific region. APJOR will place submissions in one of the following categories: General, Theoretical, OR Practice, Reviewer Survey, OR Education, and Communications (including short articles and letters). Theoretical papers should carry significant methodological developments. Emphasis is on originality, quality and importance, with particular emphasis given to the practical significance of the results. Practical papers, illustrating the application of Operation Research, are of special interest.