A convergent 3-block semi-proximal ADMM for convex minimization problems with one strongly convex block

M. Li, Defeng Sun, K.-C. Toh

Research output: Journal article publicationJournal articleAcademic researchpeer-review

48 Citations (Scopus)


© 2015 World Scientific Publishing Co. & Operational Research Society of Singapore. In this paper, we present a semi-proximal alternating direction method of multipliers (sPADMM) for solving 3-block separable convex minimization problems with the second block in the objective being a strongly convex function and one coupled linear equation constraint. By choosing the semi-proximal terms properly, we establish the global convergence of the proposed sPADMM for the step-length ? ? (0, (1+5)/2) and the penalty parameter ? (0, +?). In particular, if ? > 0 is smaller than a certain threshold and the first and third linear operators in the linear equation constraint are injective, then all the three added semi-proximal terms can be dropped and consequently, the convergent 3-block sPADMM reduces to the directly extended 3-block ADMM with ? ? (0, (1+5)/2).
Original languageEnglish
Article number1550024
JournalAsia-Pacific Journal of Operational Research
Issue number4
Publication statusPublished - 1 Jan 2015
Externally publishedYes


  • alternating direction method of multipliers
  • Convex minimization problems
  • semi-proximal
  • strongly convex

ASJC Scopus subject areas

  • Management Science and Operations Research

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