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Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
TLDR
The alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. Expand
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On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators
TLDR
This paper shows, by means of an operator called asplitting operator, that the Douglas—Rachford splitting method for finding a zero of the sum of two monotone operators is a special case of the proximal point algorithm. Expand
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Augmented Lagrangian and Alternating Direction Methods for Convex Optimization: A Tutorial and Some Illustrative Computational Results
The alternating direction of multipliers (ADMM) is a form of augmented Lagrangian algorithm that has experienced a renaissance in recent years due to its applicability to optimization problemsExpand
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Some Saddle-function splitting methods for convex programming
Consider two variations of the method of multipliers, or classical augmented Lagrangian method for convex programming. The proximal method of multipliers adjoins quadratic primal proximal terms toExpand
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Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming
TLDR
A Bregman function is a strictly convex, differentiable function that induces a well-behaved distance measure or D-function on Euclidean space, and a nonlinear version of the proximal point algorithm for convex programming . Expand
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Approximate iterations in Bregman-function-based proximal algorithms
TLDR
This paper establishes convergence of generalized Bregman-function-based proximal point algorithms when the iterates are computed only approximately. Expand
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Parallel alternating direction multiplier decomposition of convex programs
This paper describes two specializations of the alternating direction method of multipliers: the alternating step method and the epigraphic projection method. The alternating step method applies toExpand
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Pico: An Object-Oriented Framework for Parallel Branch and Bound *
TLDR
This paper describes the design of PICO, a C++ framework for implementing general parallel branch-and-bound algorithms on a wide range of parallel computing platforms. Expand
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An Alternating Direction Method for Linear Programming
This paper presents a new, simple, massively parallel algorithm for linear programming, called the alternating step method. The algorithm is unusual in that it does not maintain primal feasibility,Expand
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