Journal of Optimization Theory and Applications

, Volume 80, Issue 1, pp 39–62

Parallel alternating direction multiplier decomposition of convex programs

  • J. Eckstein
Contributed Papers

DOI: 10.1007/BF02196592

Cite this article as:
Eckstein, J. J Optim Theory Appl (1994) 80: 39. doi:10.1007/BF02196592


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 monotropic programs, while the epigraphic method applies to general block-separable convex programs, including monotropic programs as a special case. The epigraphic method resembles an earlier parallel method due to Spingarn, but solves a larger number of simpler subproblems at each iteration. This paper gives convergence results for both the alternating step and epigraphic methods, and compares their performance on random dense separable quadratic programs.

Key Words

Parallel algorithms decomposition alternating direction methods convex programming 

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • J. Eckstein
    • 1
  1. 1.Mathematical Sciences Research GroupThinking Machines CorporationCambridge

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