Some Developments of ADMM-Like Splitting Methods for Separable Convex Optimization
SUSTech and Nanjing University
2017-09-07 ~ 2017-09-07
Room 29, Quan Zhai, BICMR
Alternating direction method of multipliers (ADMM) is recognized as a powerful approach for the structured convex optimization with two separable operators. When ADMM is extended directly to a three-block separable convex minimization model, it was shown that the convergence cannot be guaranteed. This talk reports the main developments of the ADMM-like methods for the problems with three operators. By a slight correction or partly adding proximal term, the modified methods can preserve completely the advantages of the direct extension of ADMM but with guaranteed convergence. All the proposed methods belong to a unified prediction-correction framework and can be extended for solving the multi-blocks separable convex optimization. The tool for the convergence analysis is variational inequality and proximal point algorithm.