- Hybrid Middle Proximal ADMM for Linearly Constrained Convex Optimization Jianchao Bai (bjc1987163.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: 11/09/2017Entry Accepted: 11/09/2017Entry Last Modified: 02/07/2018Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.