一种新的求解单调算子零点问题的预测-校正算法框架

doi:10.15960/j.cnki.issn.1007-6093.2026.03.010

运筹学学报（中英文） ›› 2026, Vol. 30 ›› Issue (3): 170-182.doi: 10.15960/j.cnki.issn.1007-6093.2026.03.010

所属专题：运筹与管理前沿：模型、算法及其应用专辑

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一种新的求解单调算子零点问题的预测-校正算法框架

罗月英¹, 梁添喆¹, 蔡邢菊^1,2†

1. 南京师范大学数学科学学院, 江苏南京 210023;
2. 大规模复杂系统数值模拟教育部重点实验室 (南京师范大学), 江苏南京 210023

收稿日期:2026-03-30 发布日期:2026-09-12
通讯作者: 蔡邢菊 E-mail:caixingju@njnu.edu.cn
基金资助:
国家自然科学基金(No.12471290)

A new predictor-corrector algorithm framework for solving monotone inclusion problems

LUO Yueying¹, LIANG Tianzhe¹, CAI Xingju^1,2†

1. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, Jiangsu, China;
2. Key Laboratory of Numerical Simulation for Large Scale Complex Systems (Nanjing Normal University), Ministry of Education, Nanjing 210023, Jiangsu, China

Received:2026-03-30 Published:2026-09-12

摘要/Abstract

摘要： 本文针对单调算子的零点问题提出了一种新的预测-校正算法框架。多块可分凸优化问题、鞍点问题等均可转换为零点问题,并利用该算法框架设计算法。该算法框架不仅可以包含松弛的向前向后分裂算法和松弛的Davis-Yin分裂算法,还可以通过选取合适的预测算法和校正矩阵,得到Chang等(2025)中的算法3.1和5.1,从而简化其收敛性证明。

关键词: 单调算子的{零点问题}, 预测-校正算法框架, 分裂算法

Abstract: This paper proposes a novel predictor-corrector algorithm framework for monotone inclusion problems. Many classes of problems, such as multi-block separable convex optimization problems and saddle point problems, can be reformulated as monotone inclusions, and algorithms can be designed via the proposed framework. The framework not only encompasses the relaxed forward-backward splitting method and the relaxed Davis-Yin splitting method, but also reproduces Algorithm 3.1 and Algorithm 5.1 in Chang et al (2025) by appropriately selecting the predictor steps and correction matrices, thereby simplifying their convergence analysis.

Key words: monotone inclusion problems, predictor-corrector algorithm framework, splitting methods

中图分类号:

O221.2

罗月英, 梁添喆, 蔡邢菊. 一种新的求解单调算子零点问题的预测-校正算法框架[J]. 运筹学学报（中英文）, 2026, 30(3): 170-182.

LUO Yueying, LIANG Tianzhe, CAI Xingju. A new predictor-corrector algorithm framework for solving monotone inclusion problems[J]. Operations Research Transactions, 2026, 30(3): 170-182.

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一种新的求解单调算子零点问题的预测-校正算法框架

A new predictor-corrector algorithm framework for solving monotone inclusion problems

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