On the linear convergence of the alternating direction method of multipliers
نویسندگان
چکیده
منابع مشابه
Local Linear Convergence of the Alternating Direction Method of Multipliers on Quadratic or Linear Programs
We introduce a novel matrix recurrence yielding a new spectral analysis of the local transient convergence behavior of the Alternating Direction Method of Multipliers (ADMM), for the particular case of a quadratic program or a linear program. We identify a particular combination of vector iterates whose convergence can be analyzed via a spectral analysis. The theory predicts that ADMM should go...
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The formulation min x,y f(x) + g(y), subject to Ax+By = b, where f and g are extended-value convex functions, arises in many application areas such as signal processing, imaging and image processing, statistics, and machine learning either naturally or after variable splitting. In many common problems, one of the two objective functions is strictly convex and has Lipschitz continuous gradient. ...
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چکیده ندارد.
15 صفحه اولLinear Rate Convergence of the Alternating Direction Method of Multipliers for Convex Composite Programming*
In this paper, we aim to prove the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a mild calmness condition, which holds automatically for convex composite piecewise linear-quadratic programming, we establish the global Q-linear rate of convergence for a general semi-proximal ADMM w...
متن کاملOn the Convergence of Multi-Block Alternating Direction Method of Multipliers and Block Coordinate Descent Method
The paper answers several open questions of the alternating direction method of multipliers (ADMM) and the block coordinate descent (BCD) method that are now wildly used to solve large scale convex optimization problems in many fields. For ADMM, it is still lack of theoretical understanding of the algorithm when the objective function is not separable across the variables. In this paper, we ana...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2016
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-016-1034-2