報告時間: 2014年1月8日(周三) 15:40-16:40
地點:北京理工大學研究生樓103
報告人:  Prof. Yongjin Liu （劉勇進），沈陽航空航天大學理學院院長
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.

個人簡介：劉勇進，教授，碩士生導師，遼寧省“百千萬人才工程”千層次人才。2004.07畢業于大連理工大學，獲運籌學與控制論專業博士學位，博士導師是張立衛教授；2004.08-2006.07在汕頭大學從事博士后科研工作，其后在新加坡國立大學從事矩陣優化研究工作，師從Sun Defeng教授和Toh Kim-Chuan教授。其研究方向主要集中在矩陣優化理論、方法與應用，錐約束優化，數值計算等應用領域，其研究成果在Mathematical Programming (Series A)等學術期刊上共發表20余篇論文，發表論文已被他引190余次；主持國家自然科學基金項目2項，其中包括面上項目1項，青年基金項目1項；主持教育部留學歸國人員啟動基金1項，入選“2012年遼寧省高等學校杰出青年學者成長計劃”，主持博士啟動基金1項，參與多項國家自然科學基金項目。現任沈陽航空航天大學理學院院長，遼寧省數學學會常務理事，遼寧省運籌學學會常務理事。