报告人：何炳生教授（南京大学数学系）

报告时间：3月8日(本周五) 下午 4:00--5:00

报告地点：金融工程中心（览秀楼）105学术报告厅

报告题目：Customized PPA for  Convex Optimization--- Motivation and Applications

Abstract. The first order optimal conditions of the linearly constrained convex programming is a mixed monotone variational inequality in primal and dual variables. The proximal point algorithm (PPA) in Euclidean-norm is classical but abstract. Hence, PPA only plays an important theoretical role in optimization and it is rarely used in the practical scientific computation. In this talk, we introduce the recently developed customized PPA in G-norm (G is a positive definite matrix). In the frame of customized PPA, it is easy to construct the contraction-type methods for convex optimization with different linear constraints. In each iteration of the proposed methods, we need only to solve the proximal sub-problems which have the  closed-form solutions or can be efficiently solved up to a high precision.  Guided by the frame of customized PPA, the alternating direction method of multipliers is modified and it becomes more efficient. Some novel applications and numerical experiments are reported.

 

 

Prof. He received the Ph.D degree in applied mathematics from University Wuerzburg, Germany, in 1986. Since 1987 he is with the Department of Mathematics, Nanjing University. His research area include the computational mathematics and optimization. He has published over 60 refereed journal articles, including on major journals such as Mathematical Programming,  SIAM J. Optimization, SIAM J. Numerical Analysis, SIAM J. Imaging Science, SIAM J. Matrix Theory and Applications, IMA Numerical Analysis, Applied Mathematics and Optimization, Computational Optimization and Applications and JOTA. His main interest is to construct computational methods which are relative easy to understand for engineers. He authored four highly cited papers which are recognized by ISI and received ISI Citation Classic Award. Recently, Prof. He interested in the area of data science, and has three published SIAM papers which belong to the most read articles of SIAM Journals.