报告题目：Primal-Dual Splitting Methods Constructed Based on Convex Combination

报告人：杨俊锋教授、博导，南京大学

报告时间：2023年10月20日下午14:10—15:10

报告地点：数理楼306

报告对象：感兴趣的教师、研究生、本科生等

主办单位：beat365

报告人简介：杨俊锋，南京大学数学系教授，博导。2009年7月起在南京大学数学系工作，主要从事最优化计算方法及其应用研究，开发图像去模糊软件包FTVd、压缩感知一模解码软件包YALL1等。先后主持国家自然科学基金青年，面上，优秀青年科学基金等项目，曾获中国运筹学会青年科技奖等。

摘要：Consider minimizing the sum of two closed proper convex functions, one of which involves a composition with a linear transform. We propose a golden ratio primal-dual algorithm (GRPDA), which is full splitting in the sense that the per iteration cost is dominated by the evaluation of the proximal point mappings of the two component functions and two matrix-vector multiplications. We show that GRPDA converges within a broader range of parameters than the classical primal-dual algorithm. An O(1/N) ergodic convergence rate result is established based on the primal-dual gap function, where N denotes the number of iterations. When either the primal or the dual problem is strongly convex, an accelerated GRPDA is constructed to improve the ergodic convergence rate from O(1/N) to O(1/N^2). Various extensions will be discussed and numerical results will be given to demonstrate the efficiency of the proposed algorithms.