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On the Convergence Rate of Inexact Majorized sGS ADMM with Indefinite Proximal Terms for Convex Composite Programming

Author

Listed:
  • Min Li

    (School of Management and Engineering, Nanjing University, Nanjing 210093, P. R. China)

  • Zhongming Wu

    (School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China)

Abstract

In this paper, we propose an inexact majorized symmetric Gauss–Seidel (sGS) alternating direction method of multipliers (ADMM) with indefinite proximal terms for multi-block convex composite programming. This method is a specific form of the inexact majorized ADMM which is further proposed to solve a general two-block separable optimization problem. The new methods adopt certain relative error criteria to solve the involving subproblems approximately, and the step-sizes allow to choose in the scope (0, (1 + 5)/2). Under more general conditions, we establish the global convergence and Q-linear convergence rate of the proposed methods.

Suggested Citation

  • Min Li & Zhongming Wu, 2021. "On the Convergence Rate of Inexact Majorized sGS ADMM with Indefinite Proximal Terms for Convex Composite Programming," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 38(01), pages 1-34, February.
    • Handle: RePEc:wsi:apjorx:v:38:y:2021:i:01:n:s0217595920500359
    DOI: 10.1142/S0217595920500359
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    Cited by:

    1. Kuang-Yu Ding & Xin-Yee Lam & Kim-Chuan Toh, 2023. "On proximal augmented Lagrangian based decomposition methods for dual block-angular convex composite programming problems," Computational Optimization and Applications, Springer, vol. 86(1), pages 117-161, September.

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