We focus on the convergence analysis of the extended linearized alternating direction method of multipliers(L-ADMM)for solving convex minimization problems with three or more separable blocks in the objective function...We focus on the convergence analysis of the extended linearized alternating direction method of multipliers(L-ADMM)for solving convex minimization problems with three or more separable blocks in the objective functions.Previous convergence analysis of the L-ADMM needs to reduce the multi-block convex minimization problems to two blocks by grouping the variables.Moreover,there has been no rate of convergence analysis for the L-ADMM.In this paper,we construct a counter example to show the failure of convergence of the extended L-ADMM.We prove the convergence and establish the sublinear convergence rate of the extended L-ADMM under the assumptions that the proximal gradient step sizes are smaller than certain values,and any two coefficient matrices in linear constraints are orthogonal.展开更多
基金supported by the National Natural Science Foundation of China(No.61179033).
文摘We focus on the convergence analysis of the extended linearized alternating direction method of multipliers(L-ADMM)for solving convex minimization problems with three or more separable blocks in the objective functions.Previous convergence analysis of the L-ADMM needs to reduce the multi-block convex minimization problems to two blocks by grouping the variables.Moreover,there has been no rate of convergence analysis for the L-ADMM.In this paper,we construct a counter example to show the failure of convergence of the extended L-ADMM.We prove the convergence and establish the sublinear convergence rate of the extended L-ADMM under the assumptions that the proximal gradient step sizes are smaller than certain values,and any two coefficient matrices in linear constraints are orthogonal.
