報(bào)告時(shí)間: 2014年1月8日(周三) 15:40-16:40
地點(diǎn):北京理工大學(xué)研究生樓103
報(bào)告人:  Prof. Yongjin Liu （劉勇進(jìn)），沈陽航空航天大學(xué)理學(xué)院院長(zhǎng)
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(gè)人簡(jiǎn)介：劉勇進(jìn)，教授，碩士生導(dǎo)師，遼寧省“百千萬人才工程”千層次人才。2004.07畢業(yè)于大連理工大學(xué)，獲運(yùn)籌學(xué)與控制論專業(yè)博士學(xué)位，博士導(dǎo)師是張立衛(wèi)教授；2004.08-2006.07在汕頭大學(xué)從事博士后科研工作，其后在新加坡國(guó)立大學(xué)從事矩陣優(yōu)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(yōu)化理論、方法與應(yīng)用，錐約束優(yōu)化，數(shù)值計(jì)算等應(yīng)用領(lǐng)域，其研究成果在Mathematical Programming (Series A)等學(xué)術(shù)期刊上共發(fā)表20余篇論文，發(fā)表論文已被他引190余次；主持國(guó)家自然科學(xué)基金項(xiàng)目2項(xiàng)，其中包括面上項(xiàng)目1項(xiàng)，青年基金項(xiàng)目1項(xiàng)；主持教育部留學(xué)歸國(guó)人員啟動(dòng)基金1項(xiàng)，入選“2012年遼寧省高等學(xué)校杰出青年學(xué)者成長(zhǎng)計(jì)劃”，主持博士啟動(dòng)基金1項(xiàng)，參與多項(xiàng)國(guó)家自然科學(xué)基金項(xiàng)目。現(xiàn)任沈陽航空航天大學(xué)理學(xué)院院長(zhǎng)，遼寧省數(shù)學(xué)學(xué)會(huì)常務(wù)理事，遼寧省運(yùn)籌學(xué)學(xué)會(huì)常務(wù)理事。