报告时间：2020年12月5日10:00

报告地点：数计院会议室

报告题目：Alternating direction methods of multipliers for a generalized multi-facility Weber problem under gauge

报告人：南京航空航天大学蒋建林教授

邀请人：童小娇校长

报告人简介：蒋建林，南京航空航天大学教授，博士生导师，数学系主任，湖北省“楚天学者”特聘教授。2000年南京大学数学系计算数学专业获理学学士学位，2005年南京大学数学系计算数学专业获理学博士学位。研究方向为数值最优化、设施选址模型的研究与应用。在国内外正式刊物上发表学术论文40余篇。报告人与国内外学者合作密切，多次到新加坡、香港等地高校进行访问与交流。主持国家自然科学基金项目6项；参与国家自然科学基金项目3项。2014年获江苏省 “青蓝工程”培养对象。

报告摘要：A generalized multi-facility Weber problem (GMFWP), where the gauge is used to measure distances and some locational constraints are imposed to new facilities, is considered in this talk. This problem has many important applications in real situations, either itself or as subproblems. In order to solve the GMFWP efficiently, we reformulate it as a separable minimization problem and then several alternating direction methods of multipliers (ADMMs) are contributed to solving the separable problem. Specifically, for the problem with the locational constraint being $\Re^2$, a globally convergent ADMM method for two-block problem are presented; for the problem with locational constraint being a general convex set, an ADMM method for multi-block problem, which is fast but has no convergence guarantee, is adopted. One of main contribution of this paper is to propose a new linearized ADMM which is accelerated by an over-relaxation strategy for general multi-block problem and its global convergence is proved under mild assumption. We then apply it to solve the GMFWP.  Some satisfactory numerical results for numerous GMFWPs are reported, which verify the efficiency of proposed ADMM methods.