理学院“格物论坛”学术报告（六十二）

报告题目: Projection Methods for Minimizing a Finite Sum of Convex Functions

报 告 人：徐洪坤教授

报告地点：理学院A502会议室

报告时间：2018年12月18日（周二）下午：3:10-6:10

Many applied problems are formulated as a minimization problem where the objective function is a ?nite sum of convex functions and the constraint set is the intersection of ?nitely many closed convex sets. In this talk we will discuss projection methods, including sequential, parallel, and cyclic projection algorithms, for solving this sort of optimization problems. These algorithms consist of two steps. The ?rst step is an inner circle of gradient descent process to be executed through each component function and the second step is a projection process that is applied to produce the next iterate. These algorithms are proved to converge to the optimal value of the objective function by assuming boundedness of the gradients at the iterates of the component functions and the stepsizes being diminishing. It is however unknown if the iterates of the algorithms can fully converge to an optimal solution.

报告人简介：徐洪坤，博士生导师。2004年荣获南非数学学会杰出研究奖和教育部自然科学二等奖（与徐宗本、蒋耀林共同获得）。2005年当选南非科学院院士，2012年当选发展中国家科学院（最初称第三世界科学院，现更名为世界科学院）院士，2014-2016年入选汤森路透全球《高被引学者》，2017年入选科睿唯安全球《高被引学者》。已发表论文230余篇。现（曾）担任20多种（10种SCI）数学杂志编委。50余次国际学术会议邀请和主旨报告。主要研究方向：非线性泛函分析、最优化理论和算法、巴拿赫空间几何理论，非线性映像迭代方法，反问题及其正则化方法，金融数学等。