Abstract:

 

Recover bounds/relative calmness for sparse optimization models are important for theoretical and algorithmic convergence analysis in machine learning and compressed sensing. Some recent results in sparse optimization obtained by restricted isometry property and restricted eigenvalue conditions will be reviewed. Lipschitz-like property and Lipschitz continuity are at the core of stability analysis. A projectional coderivative of set-valued mappings will be discussed and applied to obtain a complete characterization for a set-valued mapping to have the Lipschitz-property relative to a closed and convex set. A mixed contingent coderivative will be discussed and applied to derive a generalized Mordukhovich criterion in infinite dimensional spaces. The Lipschitz continuity of the extended 1-norm regularization problem (or the Lasso) will be presented by virtue of polyhedral theory.

 

 

Biography:

 

Xiaoqi Yang received his PhD from The University of New South Wales in 1994. He joined Department of Applied Mathematics, The Hong Kong Polytechnic University in 1999 and now is a Professor. His research interests include variational analysis, stability theory, sparse optimization and financial optimization. He is an associate editor for several international journals, including Journal of Optimization Theory and Applications. He publishes papers in high-quality journals, such as Management Science, Mathematical Programming, SIAM Journal on Optimization. He is a co-author of three research monographs, and has over 250 publications. He has been listed as The World Top 2% most-cited scientists in recent years by Stanford University. He is the recipient of ISI Citation Classic 2000 and has been awarded The President Award for Outstanding Performance/Achievement - Research and Scholarly Activities in The Hong Kong Polytechnic University in 2000 and 2017 respectively.

 

Everyone is welcome to attend the talk!

SEEM-5202 Website: http://seminar.se.cuhk.edu.hk