Academic Report
Title: Multipliers Correction Methods for Optimization Problems with Orthogonality Constraints
Reporter: LIU Xin (Associate Research Fellow) (Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences)
Time: March 22, 2019 (Friday) AM 10:00-11:00
Location: A1101# room, Innovation Park Building
Contact: Prof. ZHANG Liwei (tel:84708351-8118)
Abstract: We consider the optimization problems with orthogonality constraints, the feasible region of which is called the Stiefel manifold. Our methods combine a function value reduction step with a multiplier correction step. The function value reduction step searches along any descent direction in the Euclidean space instead of a vector in the tangent space of the Stiefel manifold. The first-order optimality condition implies a closed-form expression for the multipliers of the orthogonality constraints. The function value reduction step can not guarantee the symmetry of the corresponding multiplier. Hence, we develop a multiplier correction step which minimize the objective function in the range space of the current iterate. Such correction step further reduces the function value and makes the corresponding multiplier expression symmetric. We also propose three algorithm which are called gradient reflection (GR), gradient projection (GP) and columnwise block coordinate descent (CBCD), respectively. Preliminary numerical experiments demonstrate that our new framework is of great potential.
The brief introduction to the reporter: Liu Xin, associate researcher, PhD supervisor, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, and winner of National Excellent Youth Science Fund. Liu Xin graduated from the School of Mathematical Sciences of Peking University in 2004, and received a doctorate from the Graduate School of the Chinese Academy of Sciences in 2009. His tutor is Academician Yuan Yaxiang. He has worked in the Institute since her graduation. During this period, he made long-term visits to ZIB Institute in Germany, RICE University in the United States and Courant Institute of New York University in the United States. His main research directions include: orthogonal constrained matrix optimization, linear and nonlinear eigenvalue problems, and their applications in electronic structure calculation; algorithms and theories of nonlinear least squares, distributed optimization algorithm design, and its applications in machine learning. Liu Xin was awarded the Excellent Youth Science Foundation of the National Natural Science Foundation of China in August 2016, the Youth Science and Technology Award of China Operational Research Society in October 2016, and the "Qimingxing" Excellent Talents Program of Beijing Branch of the Chinese Academy of Sciences in February 2017. He has been the Editorial Board of Mathematical Programming Computation since July 2015, the Director of China Operational Research Society since October 2016, the Editorial Board of Computational Mathematics since July 2017, the Vice President of Mathematics Branch of Youth Innovation Promotion Association of Chinese Academy of Sciences since May 2018, and the Special Editor of Journal of Physics since June 2018.
