报 告 人：韩德仁
报告题目：Alternating Direction Methods of Multipliers for Optimization Problems Involving Nonconvex Functions
摘要：The efficiency of the classic alternating direction method of multipliers has been exhibited by various applications for large scale separable optimization problems, both for convex objective functions and for nonconvex objective functions. While there are a lot of convergence analysis for the convex case, the nonconvex case is still an open problem and the research for this case is in its infancy. In this talk, we consider two classes of optimization problems involving nonconvex functions. The first case is the ``strongly+weakly" convex model and the second on is the general nonconvex model. For both cases, by using different analysis techniques, we prove the global convergence of the algorithms, and under some further conditions on the problem's data, we also analyze the convergence rate.
报告人简介：韩德仁，北京航空航天大学数学与系统科学学院院长、博士生导师、教授。2002年获南京大学计算数学博士学位。从事大规模优化问题、变分不等式问题的数值方法的研究工作。在Mathematical Programming, Numerische Mathematik, SIAM Journal on Numerical Analysis, Mathematics of Computation等计算数学、运筹学重要杂志以发表多篇学术论文。担任中国运筹学会理事、数学规划分会常务理事；《计算数学》、《Journal of the Operations Research Society of China》编委。