报告题目：Regularized splitting method for three operators inclusion system of “two maximal monotone + one cocoercive” and its applications
时 间：2025年11月14日 (星期五) 15:00
地 点：科研楼18号楼1102
主 办：数学与统计学院、分析数学及应用教育部重点实验室、福建省分析数学及应用重点实验室、统计学与人工智能福建省高校重点实验室、福建省应用数学中心（福建师范大学）
参加对象：感兴趣的老师和研究生
报告摘要：This paper considers finding a zero point of A + B + C, where A and C are maximal monotone and B is ξ -cocoercive. The three-operator splitting method (TSM), proposed by Davis and Yin, is a popular algorithm for solving this problem. Observing that the x-sequence and the y-sequence in TSM have the same accumulation point and B’s information is only utilized in the second subproblem, this work proposes a new splitting method named the regularized splitting method (RSM), where “x = y” is introduced as a penalty term and the forward step is also employed in the first subproblem. The penalty term can balance the differences between the two subproblems and the additional forward step enables utilizing B’s information in both subproblems simultaneously. We establish the convergence of the proposed method and demonstrate its sublinear convergence rate concerning the fixed-point residuals, assuming mild conditions in an infinite dimensional Hilbert space. As an application, we use RSM to solve zero point problems involving multiple operators. By introducing a new space reconstruction method, we transform the problem of multiple operators into a problem of three operators and derive a distributed version of the RSM. We validate our method ’ s efficiency through applications to mean-variance optimization, inverse problems in imaging, and the softmargin support vector machine problem with nonsmooth hinge loss functions, showcasing its superior performance compared to existing algorithms in the literature.
报告人简介：蔡邢菊，南京师范大学教授，博导。主要从事最优化理论与算法、变分不等式、数值优化方向研究工作。主持多项国家基金，获江苏省科技进步奖一等奖一项，发表SCI论文70余篇。担任中国运筹学会副秘书长、算法软件与应用分会常务理事兼秘书长、数学规划分会常务理事，江苏省运筹学会理事长。