报 告 人：Toh Kim Chuan教授（新加坡国立大学），Beale--Orchard- Hays奖和Fakas奖获得者
时间：2018年12月20 日（下午14:30-15:50）
地点：数学院203报告厅
报告题目：On the efficient computation of a generalized Jacobian of the projector over the Birkhoff polytope
报告摘要： We derive an explicit formula, as well as an efficient procedure, for constructing a generalized Jacobian for the projector of a given square matrix onto the Birkhoff polytope, i.e., the set of doubly stochastic matrices. To guarantee the high efficiency of our procedure, a semismooth Newton method for solving the dual of the projection problem is proposed and efficiently implemented. Extensive numerical experiments are presented to demonstrate the merits and effectiveness of our method by comparing its performance against other powerful solvers such as the commercial software Gurobi and the academic code PPROJ [ Hager and Zhang, SIAM Journal on Optimization, 26 (2016), pp.~1773--1798]. In particular, our algorithm is able to solve the projection problem with over one billion variables and nonnegative constraints to a very high accuracy in less than 15 minutes on a modest desktop computer. More importantly, based on our efficient computation of the projections and their generalized Jacobians, we can design a highly efficient augmented Lagrangian method (ALM) for solving a class of convex quadratic programming (QP) problems constrained by the Birkhoff polytope. The resulted ALM is demonstrated to be much more efficient than Gurobi in solving a collection of QP problems arising from the relaxation of quadratic assignment problems. [Joint work with Xudong Li and Defeng Sun]
报告人简介：Toh Kim Chuan（卓金全）教授1990年本科毕业于新加坡国立大学数学系，1992年在新加坡国立大学数学系获硕士学位，1996在美国康奈尔大学应用数学中心获博士学位（导师: Nick Trefethen），并开始在新加坡国立大学数学系工作，现任新加坡国立大学数学系教务长讲座教授（Provost’s Chair Professor）。卓教授是国际知名数值优化专家，主要致力于矩阵优化、凸规划等方面的算法设计、分析与实现。他曾多次在重要的国际学术组织和学术会议中担任要职，并入选美国工业与应用数学学会会士（SIAM Fellow, 2018），2017年获得IFORMS颁发的Fakas奖， 2018年获得国际数学规划Beale—Orchard- Hays奖。他现任《Mathematical Programming》，《Mathematical Programming Computation》以及《SIAM Journal on Optimization》等连续优化方向重要学术期刊的编委。卓教授及其合作者研制的软件如SDPT3，SDPNAL/SDPNAL+, LassoNAL等被学术界和工业界广泛使用。
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