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- Stephen P. Boyd, Neal Parikh, Eric Chu, Borja Peleato, Jonathan Eckstein
- Foundations and Trends in Machine Learning
- 2011

Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or… (More)

- Jonathan Eckstein, Dimitri P. Bertsekas
- Math. Program.
- 1992

This paper shows, by means of a new type of operator called a splitting 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. Therefore, applications of Douglas-Rachford splitting, such as the alternating direction method of multipliers for convex… (More)

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 problems arising from “big data” and image processing applications, and the relative ease with which it may be implemented in parallel and distributed computational… (More)

- Jonathan Eckstein
- Math. Oper. Res.
- 1993

- Jonathan Eckstein
- Math. Program.
- 1998

This paper establishes convergence of generalized Bregman-function-based proximal point algorithms when the iterates are computed only approximately. The problem being solved is modeled as a general maximal monotone operator, and need not reduce to minimization of a function. The accuracy conditions on the iterates resemble those required for the classical… (More)

- Jonathan Eckstein, Peter L. Hammer, Ying Liu, Mikhail Nediak, Bruno Simeone
- Comp. Opt. and Appl.
- 2002

- Dimitri P. Bertsekas, Jonathan Eckstein
- Math. Program.
- 1988

We review a class of recently-proposed linear-cost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of e-complementary slackness, and most do not explicitly manipulate any "global" objects such as paths, trees, or cuts. Interestingly, these methods have stimulated a large number of new serial… (More)

- Paulo J. S. Silva, Jonathan Eckstein
- Comp. Opt. and Appl.
- 2006

- Jonathan Eckstein
- SIAM Journal on Optimization
- 1994

We describe a general projective framework for finding a zero of the sum of n maximal monotone operators over a real Hilbert space. Unlike prior methods for this problem, we neither assume n = 2 nor first reduce the problem to the case n = 2. Our analysis defines a closed convex extended solution set for which we can construct a separating hyperplane by… (More)