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A Linearized Alternating Direction Method of Multipliers with Substitution Procedure

Author

Listed:
  • Miantao Chao

    (Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China)

  • Caozong Cheng

    (Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China)

  • Haibin Zhang

    (Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China)

Abstract

We consider the linearly constrained separable convex programming problem whose objective function is separable into m individual convex functions with non-overlapping variables. The alternating direction method of multipliers (ADMM) has been well studied in the literature for the special case m = 2, but the direct extension of ADMM for the general case m ≥ 2 is not necessarily convergent. In this paper, we propose a new linearized ADMM-based contraction type algorithms for the general case m ≥ 2. For the proposed algorithm, we prove its convergence via the analytic framework of contractive type methods and we derive a worst-case O(1/t) convergence rate in ergodic sense. Finally, numerical results are reported to demonstrate the effectiveness of the proposed algorithm.

Suggested Citation

  • Miantao Chao & Caozong Cheng & Haibin Zhang, 2015. "A Linearized Alternating Direction Method of Multipliers with Substitution Procedure," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-19.
    • Handle: RePEc:wsi:apjorx:v:32:y:2015:i:03:n:s0217595915500116
    DOI: 10.1142/S0217595915500116
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