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Faster convergence rates of relaxed Peaceman-Rachford and ADMM under regularity assumptions. (English) Zbl 1379.65035
The authors present a comprehensive rate analysis of the Douglas-Rachford splitting, the Peaceman-Rachford splitting and the alternating direction method of multipliers (ADDM) under regularity assumptions such as strong convexity, Lipschitz differentiability and bounded linear regularity. They show that the relaxed Peaceman-Rachford splitting and the alternating direction method of multipliers converge at an improving rate upon the worst-case rates which hold in the absence of the mentioned regularity.
This article is well written, structured and explained, it contains eight sections: Section 1 on Introduction, Section 2 on Preliminaries, Section 3 on Strong convexity, Section 4 on Lipschitz gradients, Section 5 on Linear convergence, Section 6 on Feasibility problems with regularity, Section 7 on From relaxed Peaceman-Rachford splitting to alternating direction method of multipliers, and Section 8 on Conclusion.

MSC:
65K05 Numerical mathematical programming methods
90C25 Convex programming
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