On the convergence properties of a majorized ADMM for linearly constrained convex optimization problems with coupled objective functions
Optimization and Control
2017-01-18 v1
Abstract
In this paper, we establish the convergence properties for a majorized alternating direction method of multipliers (ADMM) for linearly constrained convex optimization problems whose objectives contain coupled functions. Our convergence analysis relies on the generalized Mean-Value Theorem which plays an important role to properly control the cross terms due to the presence of coupled objective functions. Our results in particular show that directly applying 2-block ADMM with a large step length to the linearly constrained convex optimization problem with a quadratically coupled objective function is convergent under mild conditions. We also provide several iteration complexity results for the algorithm.
Keywords
Cite
@article{arxiv.1502.00098,
title = {On the convergence properties of a majorized ADMM for linearly constrained convex optimization problems with coupled objective functions},
author = {Ying Cui and Xudong Li and Defeng Sun and Kim-Chuan Toh},
journal= {arXiv preprint arXiv:1502.00098},
year = {2017}
}