On the Convergence Properties of a Majorized Alternating Direction Method of Multipliers for Linearly Constrained Convex Optimization Problems with Coupled Objective Functions

Y. Cui, X. Li, Defeng Sun, K.-C. Toh

Research output: Journal article publicationJournal articleAcademic researchpeer-review

26 Citations (Scopus)


© 2016, Springer Science+Business Media New York. In this paper, we establish the convergence properties for a majorized alternating direction method of multipliers for linearly constrained convex optimization problems, whose objectives contain coupled functions. Our convergence analysis relies on the generalized Mean-Value Theorem, which plays an important role to properly control the cross terms due to the presence of coupled objective functions. Our results, in particular, show that directly applying two-block alternating direction method of multipliers with a large step length of the golden ratio to the linearly constrained convex optimization problem with a quadratically coupled objective function is convergent under mild conditions. We also provide several iteration complexity results for the algorithm.
Original languageEnglish
Pages (from-to)1013-1041
Number of pages29
JournalJournal of Optimization Theory and Applications
Issue number3
Publication statusPublished - 1 Jun 2016
Externally publishedYes


  • Convex quadratic programming
  • Coupled objective function
  • Iteration complexity
  • Majorization
  • Nonsmooth analysis

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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