Academic Report
Title: Some new optimization theory for convergence analysis of first-order algorithms
Reporter: ZHANG Jin (Hong Kong Baptist University)
Time: November 9, 2018 (Friday) PM 15:30-16:30
Location: A1101# room, Innovation Park Building
Contact: LIU Yongchao (tel:84708351-8141)
Abstract: We present some new theoretical results for the topics of optimality conditions, constraint qualifications and error bounds in optimization, and show how these theoretical results can be used for analyzing the convergence of some very popular first-order algorithms which have been finding wide applications in data science domains. Some fundamental models such as the LASSO and grouped LASSO are studied, and it is shown that the linear convergence can be obtained if some algorithms are implemented for these models such as the proximal gradient method, the proximal alternating linearized minimization algorithm and the randomized block coordinate proximal gradient method. We provide a novel analytic framework based on variational analysis techniques (e.g., error bound, calmness, metric subregularity) for the convergence analysis of first-order algorithms. By this new analytic framework, we significantly improve some convergence rate results in the literature and obtain some new results.
The brief introduction to the reporter: Zhang Jin, born in March 1986, is an assistant professor of research at Hong Kong Baptist University. He received his Bachelor of Arts from the School of Humanities and Social Sciences of Dalian University of Technology in 2007, his Master of Science degree from the School of Mathematical Sciences of Dalian University of Technology in 2010, and his Ph.D. in Applied Mathematics from the Department of Mathematics and Statistics of Victoria University of Canada in December 2014. He entered the Mathematics Department of Hong Kong Baptist University in July 2015. Zhang Jin is mainly engaged in optimization theory, especially optimization conditions and constraint specifications. He has published more than 10 SCI retrieval papers, many of which have been published in the top journals of Mathematical Programming, SIAM Journal on Optimization and other optimization fields.
