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Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers

- Stephen P. Boyd, N. Parikh, E. Chu, B. Peleato, Jonathan Eckstein
- Computer Science
- Found. Trends Mach. Learn.
- 23 May 2011

TLDR

12,265 2868- PDF

On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators

- Jonathan Eckstein, D. Bertsekas
- Computer Science, Mathematics
- Math. Program.
- 6 June 1992

TLDR

2,311 255- PDF

Splitting methods for monotone operators with applications to parallel optimization

- Jonathan Eckstein
- Mathematics
- 1989

280 27

Augmented Lagrangian and Alternating Direction Methods for Convex Optimization: A Tutorial and Some Illustrative Computational Results

- Jonathan Eckstein
- Mathematics
- 2012

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… Expand

198 20- PDF

Some Saddle-function splitting methods for convex programming

- Jonathan Eckstein
- Mathematics
- 1994

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 to… Expand

116 18

Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming

- Jonathan Eckstein
- Mathematics, Computer Science
- Math. Oper. Res.
- 1 February 1993

TLDR

315 17

Approximate iterations in Bregman-function-based proximal algorithms

- Jonathan Eckstein
- Mathematics, Computer Science
- Math. Program.
- 1 September 1998

TLDR

161 14

Parallel alternating direction multiplier decomposition of convex programs

- Jonathan Eckstein
- Mathematics
- 1994

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 to… Expand

131 11

Pico: An Object-Oriented Framework for Parallel Branch and Bound *

- Jonathan Eckstein, C. Phillips, W. Hart
- Computer Science
- 2001

TLDR

112 10

An Alternating Direction Method for Linear Programming

- Jonathan Eckstein, D. Bertsekas, Decision Systems.
- Mathematics
- 1990

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

56 10

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