报告时间: 2014年1月8日(周三) 15:40-16:40
地点:北京理工大学研究生楼103
报告人:  Prof. Yongjin Liu （刘勇进），沈阳航空航天大学理学院院长
Title: A Semismooth Newton-CG Based Dual PPA for Matrix Spectral Norm Approximation Problems

Abstract: We consider a class of matrix spectral norm approximation problems for finding an affine combination of given matrices having the minimal spectral norm subject to some prescribed linear equality and inequality constraints. These problems arise often in numerical algebra, engineering and other areas, such as finding Chebyshev polynomials of matrices and fastest mixing Markov chain models. Based on classical analysis of proximal point algorithms (PPAs) and recent developments on semismooth analysis of nonseparable spectral operators, we propose a semismooth Newton-CG based dual PPA for solving the matrix norm approximation problems. Furthermore, when the primal constraint nondegeneracy condition holds for the subproblems, our semismooth Newton-CG method is proven to have at least a superlinear convergence rate. We also design efficient implementations for our proposed algorithm to solve a variety of instances and compare its performance with the nowadays popular first order alternating direction method of multipliers (ADMM). The results show that our algorithm substantially outperforms the ADMM, especially for the constrained cases and it is able to solve the problems robustly and efficiently to a relatively high accuracy.

个人简介：刘勇进，教授，硕士生导师，辽宁省“百千万人才工程”千层次人才。2004.07毕业于大连理工大学，获运筹学与控制论专业博士学位，博士导师是张立卫教授；2004.08-2006.07在汕头大学从事博士后科研工作，其后在新加坡国立大学从事矩阵优化研究工作，师从Sun Defeng教授和Toh Kim-Chuan教授。其研究方向主要集中在矩阵优化理论、方法与应用，锥约束优化，数值计算等应用领域，其研究成果在Mathematical Programming (Series A)等学术期刊上共发表20余篇论文，发表论文已被他引190余次；主持国家自然科学基金项目2项，其中包括面上项目1项，青年基金项目1项；主持教育部留学归国人员启动基金1项，入选“2012年辽宁省高等学校杰出青年学者成长计划”，主持博士启动基金1项，参与多项国家自然科学基金项目。现任沈阳航空航天大学理学院院长，辽宁省数学学会常务理事，辽宁省运筹学学会常务理事。