A Linear Convergence Result for the Jacobi-Proximal Alternating Direction Method of Multipliers

Hyelin Choi; Woocheol Choi

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arXiv · 2503.18601

A Linear Convergence Result for the Jacobi-Proximal Alternating Direction Method of Multipliers

Hyelin Choi·Woocheol Choi

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Abstract

In this paper, we analyze the convergence rate of the Jacobi-Proximal Alternating Direction Method of Multipliers (ADMM) initially introduced by Deng et al. for the block-structured optimization problem with linear constraint. The algorithm is well-suited for parallel implementation and widely used for large-scale multi-block optimization problems. While the o(1/k) convergence of the Jacobi-Proximal ADMM for the case $N \geq 3$ has been well-established in the previous work, to the best of our knowledge, its linear convergence for $N \geq 3$ remains unproven. We establish the linear convergence of the algorithm when the cost functions are strongly convex and smooth. Numerical experiments are presented supporting the convergence result.

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BibTeX RIS

Hyelin Choi, Woocheol Choi. 2025-03-24. A Linear Convergence Result for the Jacobi-Proximal Alternating Direction Method of Multipliers. https://arxiv.org/abs/2503.18601

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