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New Variants and Convergence Properties of the Alternating Direction Method of Multipliers (ADMM)

Tuesday, May 3, 2016 - 1:25pm - 2:25pm
Lind 305
Shuzhong Zhang (University of Minnesota, Twin Cities)
The Alternating Direction Method of Multipliers (ADMM) has been a very popular choice for solving large scale constrained optimization models arising from many application domains, including statistical and machine learning, image and signal processing, biological and medical applications. Many variants of the method have been proposed to adaptively account for specific settings relevant to different applications. In this talk we aim to survey some of the recent developments along this line, and present new convergence results. It is well known that the multi-block version of the ADMM may fail to converge in general. We show how to overcome this difficulty by incorporating a randomization procedure in the selection of the block variables. Time permitting, I shall also present some very recent results regarding iteration complexity bounds for the ADMM applied to solve nonconvex optimization models.

Based on the joint research with: Xiang Gao, Yangyang Xu, Bo Jiang, and Shiqian Ma