Abstract:We consider the problem of finite-sum non-smooth convex optimization with general linear constraints, where the objective function summands are only accessible through their proximal operators. To solve it, we propose an Anderson accelerated Douglas-Rachford splitting (A2DR) algorithm, which combines the scalability of Douglas-Rachford splitting and the fast convergence of Anderson acceleration. We show that A2DR either globally converges or provides a certificate of infeasibility/unboundedness under very mild conditions. We describe an open-source implementation (https://github.com/cvxgrp/a2dr) and demonstrate its outstanding performance on a wide range of examples. The talk is mainly based on the joint work [SIAM Journal on Scientific Computing, 42.6 (2020): A3560–A3583] with Anqi Fu and Stephen Boyd.

Short Bio:Junzi Zhang is currently working at Amazon Advertising as an Applied Scientist. He got his Ph.D. degree in Computational Mathematics at Stanford University, advised by Prof. Stephen P. Boyd from Stanford Department of Electrical Engineering. He has also been working closely with Prof. Xin Guo and Prof. Mykel J. Kochenderfer. Before coming to Stanford, he obtained a B.S. degree in applied mathematics from School of Mathematical Sciences, Peking University, where he conducted his undergraduate research under the supervision of Prof. Zaiwen Wen and Prof. Pingwen Zhang. His research has been focused on the design and analysis of optimization algorithms and software, and extends broadly into the fields of machine learning, causal inference and decision-making systems (especially reinforcement learning). He is also recently extending his research to federated optimization, predictive modeling and digital advertising. His research had been partly supported by Stanford Graduate Fellowship. More information can be found on his personal website at https://web.stanford.edu/~junziz/index.html.