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