The alternating direction method of multipliers (ADMM) is an algorithm that solves convex optimization problems by breaking them into smaller pieces, each of which are then easier to handle. It takes the form of a decomposition-coordination procedure, in which the solutions to small local subproblems are coordinated to find a solution to a large global problem. ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods for constrained optimization. It turns out to be equivalent or closely related to many other algorithms as well, such as Douglas-Rachford splitting from numerical analysis, Spingarn’s method of partial inverses, Dykstra’s alternating projections method, Bregman iterative algorithms for l1 problems in signal processing, proximal methods, and many others.
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