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Hybrid Middle Proximal ADMM for Linearly Constrained Convex Optimization

Jianchao Bai (bjc1987***at***163.com)

Abstract: This paper focuses on a family of Middle Proximal Alternating Direction Method of Multipliers (MP-ADMM) for solving multi-block separable convex optimization subject to linearly constraints and structured constraints. This one-parameter family of MP-ADMM combines both Jacobi and Gauss-Seidel type of ADMM and proximal point techniques are only applied to the middle subproblems to promote its convergence. We analyze the global convergence as well as the worst-case ${\mathcal O} (1/t)$ ergodic convergence rate of this new algorithm, where $t$ is the iteration number. Moreover, linear convergence of the algorithm is also established under the assumption that the sub-differential of each component function in the objective function is piece-wise linear. {\color{red}Besides, a linearized version of MP-ADMM is also discussed to accelerate the convergence.} Compared with several state-of-the-art algorithms in the literature, this new MP-ADMM performs very well for solving a latent variable Gaussian graphical model selection problem arising in statistical learning.

Keywords: Alternating direction method of multipliers; Combination technique; Proximal term; Variational inequality; Global convergence

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: submitted

Download: [PDF]

Entry Submitted: 11/09/2017
Entry Accepted: 11/09/2017
Entry Last Modified: 02/07/2018

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