讨论班

Studying the linear convergence of ADMM for structured convex optimization via variational analysis

2019-10-21 16:43

报告人: 张进

报告人单位: 南方科技大学

时间: 2019-10-22 15:30-16:30

地点: 卫津路校区14-202

开始时间: 15:30

报告人简介: 博士

年: 2019

日月: 10.22

Despite the rich literature, the linear convergence of alternating direction method of multipliers (ADMM) has not been fully understood even for the convex case. For example, the linear convergence of ADMM can be empirically observed in a wide range of applications arising in statistics, machine learning, and related areas, while existing theoretical results seem to be too stringent to be satisfied or too ambiguous to be checked and thus why the ADMM performs linear convergence for these applications still seems to be unclear. In this paper, we systematically study the linear convergence of ADMM in the context of convex optimization through the lens of variational analysis. We show that the linear convergence of ADMM can be guaranteed without the strong convexity of objective functions together with the full rank assumption of the coefficient matrices, or the full polyhedricity assumption of their subdifferential; and it is possible to discern the linear convergence for various concrete applications, especially for some representative models arising in statistical learning. We use some variational analysis techniques sophisticatedly; and our analysis is conducted in the most general proximal version of ADMM with Fortin and Glowinski's larger step size so that all major variants of the ADMM known in the literature are covered.


Contact us

Add:Building 32, The School of Mathematics, Tianjin University Beiyangyuan Campus,

        No. 135, Ya Guan Road, Jinnan District, Tianjin, PRC 

Tel:022-27403615   Mail:maths@tju.edu.cn