12月15日:杨俊峰 、陈彩华 、郦旭东
报告题目：On Progressive Hedging Algorithm and Douglas-Rachford Operator Splitting Method for Multistage Stochastic Variational Inequalities
报告人：杨俊峰 教授 南京大学数学系
Junfeng Yang, Professor, Department of Mathematics, Nanjing University. He received his MSc in 2006 under the supervision of Prof. Yaxiang Yuan (AMSS, CAS) and PhD in 2009 under the supervision of Prof. Bingsheng He (Nanjing University) and Prof. Yin Zhang (Rice University). He is mainly interested in designing, analyzing and implementing fast algorithms for solving optimization problems arising from signal and image processing, compressive sensing and sparse optimization, etc. Together with collaborators, he has developed Matlab packages FTVd for image deblurring and YALL1 for L1 optimization in compressive sensing.
Progressive hedging algorithm (PHA) was originally proposed by Rockafellar and Wets in 1991 for stochastic convex optimization. Recently, it was extended to solving stochastic variational inequality problems by Rockafellar and Sun. It is known that PHA is an application of the proximal point algorithm. In this talk,we establish its connections with the alternating direction method of multipliers and Douglas-Rachford operator splitting method. These results sharpens our understanding to PHA and enable us to consider some extensions. This is a joint work with Xiaojun Chen and Defeng Sun.
报告题目：Convergence and Convergence Rate Analysis of ADMM for Regularized Matrix Factorization报告人：陈彩华 副教授 南京大学工程管理学院
代表性论文发表在在Mathematical Programming, SIAM Journal on Optimizaiton, SIAM Journal on Imaging Science, IMA Journal of Numerical Analysis等国际期刊， 另有2篇论文入选ESI高被引论文。
In this talk, we consider the matrix factorization model with several different regularizers. Under certain conditions, error bound and K-L property with the exponent 1/2 are established for the models. With this, we are able to prove the global and locally linear convergence of alternating direction method of multipliers (ADMM) without assuming the boundedness of the sequence.
报告题目：On the Efficient Computation of a Generalized Jacobian of the Projector Over the Birkhoff Polytope报告人：郦旭东 博士 Princeton University
Dr. Li is currently a Postdoctoral Research Associate in the Department of Operations Research and Financial Engineering at Princeton University. Previously, he was a research fellow at the Department of Mathematics, National University of Singapore. He obtained my Ph.D. degree in Optimization from National University of Singapore in 2015. His current research focuses on designing efficient algorithms and software for data-driven optimization problems, particularly large-scale optimization problems arising from data analysis and machine learning; and large-scale matrix optimization problems, such as linear semidefinite programming (SDP) and convex quadratic semidefinite programming (QSDP).
In this talk, 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, 2016]. 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. In order to further demonstrate the importance of our procedure, we also propose 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. This talk is based on a joint work with Defeng Sun and Kim-Chuan Toh.