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Inexact alternating direction methods of multipliers for separable convex optimization

Author

Listed:
  • William W. Hager

    (University of Florida)

  • Hongchao Zhang

    (Louisiana State University)

Abstract

Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach involves linearized subproblems, a back substitution step, and either gradient or accelerated gradient techniques. Global convergence is established. The methods are particularly useful when the ADMM subproblems do not have closed form solution or when the solution of the subproblems is expensive. Numerical experiments based on image reconstruction problems show the effectiveness of the proposed methods.

Suggested Citation

  • William W. Hager & Hongchao Zhang, 2019. "Inexact alternating direction methods of multipliers for separable convex optimization," Computational Optimization and Applications, Springer, vol. 73(1), pages 201-235, May.
    • Handle: RePEc:spr:coopap:v:73:y:2019:i:1:d:10.1007_s10589-019-00072-2
    DOI: 10.1007/s10589-019-00072-2
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    References listed on IDEAS

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    1. Min Li & Defeng Sun & Kim-Chuan Toh, 2015. "A Convergent 3-Block Semi-Proximal ADMM for Convex Minimization Problems with One Strongly Convex Block," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-19.
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    8. Jueyou Li & Guo Chen & Zhaoyang Dong & Zhiyou Wu, 2016. "A fast dual proximal-gradient method for separable convex optimization with linear coupled constraints," Computational Optimization and Applications, Springer, vol. 64(3), pages 671-697, July.
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    Cited by:

    1. William W. Hager & Hongchao Zhang, 2020. "Convergence rates for an inexact ADMM applied to separable convex optimization," Computational Optimization and Applications, Springer, vol. 77(3), pages 729-754, December.
    2. Jianchao Bai & William W. Hager & Hongchao Zhang, 2022. "An inexact accelerated stochastic ADMM for separable convex optimization," Computational Optimization and Applications, Springer, vol. 81(2), pages 479-518, March.

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