摘要：

Many applied problems are formulated as a minimization problem where the objective function is a finite sum of convex functions and the constraint set is the intersection of finitely 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 first 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.

时间：2018年5月29日15：00

地点：下沙校区D楼204室

报告人简介：

徐洪坤教授现为杭州电子大学教授，世界科学院院士。徐洪坤教授曾先后就职于华东理工大学、西班牙Sevilla 大学、加拿大Dalhousie大学、南非KwaZulu-Natal大学、沙特阿拉伯King Saud大学和台湾中山大学，曾任台湾中山大学应用数学系主任和理学院院长，2005年当选为南非科学院院士，2012年当选为世界科学院院士。徐洪坤教授多年来一直致力于非线性泛函分析与优化、非线性反问题之迭代方法和金融数学中的定价问题的研究，迄今已发表论文近250篇，在2012年ISI的数学家排名中列第15位，多次成为ESI的高引用学者。