报告题目：A highly efficient semismooth Netwon augmented Lagrangian method for solving Lasso problems

报  告  人：Toh Kim Chuan

报告时间：12月16日（星期五）上午10:45-11:45

报告地点：清水河校区主楼A1-512 (数学学院会议室)

报告摘要：We develop a fast and robust algorithm for solving large scale convex composite optimization models with an emphasis on the L1-regularized least squares regression (Lasso) problems. Despite the fact that there exist a large number of solvers in the literature for the Lasso problems,

we found that no solver can efficiently handle difficult large scale regression problems with

real data. By leveraging on available error bound results to realize the asymptotic suplinear

convergence property of the augmented Lagrangian algorithm, and by exploiting the second

order sparsity of the problem through the semismooth Newton method, we are able to propose

an algorithm, called SSNAL, to efficiently solve the aforementioned difficult problems. Under

very mild conditions, which hold automatically for Lasso problems, both the primal and the

dual iteration sequences generated by SSNAL possess a remarkably fast linear convergence rate,

which can even be made to be superlinear asymptotically. Numerical comparisons between our

approach and a number of state-of-the-art solvers, on real data sets, are presented to demonstrate

the high efficiency and robustness of our proposed algorithm in solving difficult large scale Lasso

problems

报告人简介：Toh Kim Chuan 教授1990年毕业于新加坡国立大学数学系，1996年于美国康奈尔大学数学系获得博士学位，现为新加坡国立大学数学系教授。Toh教授是国际著名运筹学专家，是著名算法---SDPT3的开发者。曾在SIAM Review, SIAM Optimization, Mathematical Programming 上发表文章80余篇。Toh教授先后担任SIAM Optimization, Mathematical Programming Computation, Foundations and Trends in Optimization等十余个杂志编委。2016年国际连续优化颁奖委员会成员。2010年SIAM年会的主旨报告人。

更多信息见http://www.math.nus.edu.sg/~mattohkc/.