2022/04/04 by Hongwu Li, Haibin Zhang, Li, Hongwu +3
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Direction-of-Arrival Estimation Techniques #FOS: Mathematics #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2204.01315
openalex publication_date 2022/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The generalized alternating direction method of multipliers (ADMM) of Xiao et al. [\tt Math. Prog. Comput., 2018] aims at the two-block linearly constrained composite convex programming problem, in which each block is in the form of "nonsmooth + quadratic". However, in the case of non-quadratic (but smooth), this method may fail unless the favorable structure of 'nonsmooth + smooth' is no longer used. This paper aims to remedy this defect by using a majorized technique to approximate the augmented Lagrangian function, so that the corresponding subprobllem can be decomposed into some smaller problems and then solved separately. Furthermore, the recent symmetric Gauss-Seidel (sGS) decomposition theorem guarantees the equivalence between the bigger subproblem and these smaller ones. This paper focuses on convergence analysis, that is, we prove that the sequence generated by the proposed method converges globally to a Karush-Kuhn-Tucker point of the considered problem. Finally, we do some numerical experiments on a kind of simulated convex composite optimization problems which illustrate that the proposed method is more efficient than its compared ones.