Title: Error bounds and the superlinear convergence rates of the augmented Lagrangian methods
Speaker: Defeng Sun, Department of Applied Mathematics, The Hong Kong Polytechnic University
Time：2018-6-7， 14：30—16：00
Place：Wegetang-- 417
Abstract: Recently, a series of efficient solvers based on the augmented Lagrangian method (ALM) have been successfully developed for solving large scales convex optimization problems. However, due to the possible lack of primal-dual-type error bounds, the superlinear convergence for the Karush-Kuhn-Tucker residuals of the sequence generated by the ALM for solving convex composite conic programming has long been an open question. In this talk, we shall explain how to resolve this issue by only assuming a mild dual type error bound condition under easy-to-implement stopping criteria for the augmented Lagrangian subproblems. This discovery helps us to gain insightful interpretations on the impressive numerical performance of the existing ALM based solvers and guides us to employ the ALM properly for the unexplored optimization problems.
Biodata: Professor Sun Defeng is currently Chair Professor of Applied Optimization and Operations Research at the Hong Kong Polytechnic University. Before moving to Hong Kong in August 2017, Professor Sun served as Professor at Department of Mathematics, National University of Singapore, Deputy Director (Research) at the NUS Risk Management Institute and Program Director for its Master of Financial Engineering program. He mainly publishes in continuous optimization. He has written a number of software for solving large-scale complex optimization problems, including SDPNAL/SDPNAL+ for general purpose large scale semidefinite programming, codes for correlation matrix calibrations and most recently the packages including LassoNAL for various statistical regression models. Currently Professor Sun focuses on establishing the foundation for the next generation methodologies for big data optimization and applications. Professor Sun has actively involved in many professional activities. He served as editor-in-chief of Asia-Pacific Journal of Operational Research from 2011 to 2013 and he now serves as associate editor of Mathematical Programming, SIAM Journal on Optimization, Journal of the Operations Research Society of China, Journal of Computational Mathematics, and Science China:Mathematics.