ADMM

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 has recently found wide application in a number of areas. On this page, we provide a few links to to interesting applications and implementations of the method, along with a few primary references.

ADMM is used in a large number of papers at this point, so it is impossible to be comprehensive here. We only intend to highlight a few representative examples in different areas. To keep the listing light, we have only listed more detailed bibliographic information for papers that are not easy to find online; in any case, the information given should be more than enough to track down the papers.

Main references

Software

Classic papers

On the numerical solution of heat conduction problems in two and three space variables J. Douglas and H. H. Rachford, Transactions of the American Mathematical Society, 1956

Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéares R. Glowinski and A. Marrocco, Revue Française d'Automatique, Informatique, et Recherche Opérationelle, 1975

A dual algorithm for the solution of nonlinear variational problems via finite element approximations D. Gabay and B. Mercier, Computers and Mathematics with Applications, 1976

Splitting algorithms for the sum of two nonlinear operators P. L. Lions and B. Mercier, 1979

On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators J. Eckstein and D. Bertsekas, Mathematical Programming, 1992

Generic problems

Applications

Theory and variations