On the convergence properties of a majorized ADMM for linearly constrained convex optimization problems with coupled objective functions

Ying Cui; Xudong Li; Defeng Sun; Kim-Chuan Toh

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arXiv · 1502.00098

On the convergence properties of a majorized ADMM for linearly constrained convex optimization problems with coupled objective functions

Ying Cui·Xudong Li·Defeng Sun·Kim-Chuan Toh

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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.

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BibTeX RIS

Ying Cui, Xudong Li, Defeng Sun, Kim-Chuan Toh. 2015-01-31. On the convergence properties of a majorized ADMM for linearly constrained convex optimization problems with coupled objective functions. https://arxiv.org/abs/1502.00098

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