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An Inexact Dual Fast Gradient-Projection Method for Separable Convex Optimization with Linear Coupled Constraints

Author

Listed:
  • Jueyou Li

    (Chongqing Normal University)

  • Zhiyou Wu

    (Chongqing Normal University)

  • Changzhi Wu

    (School of Built Environment, Curtin University)

  • Qiang Long

    (Southwest University of Science and Technology)

  • Xiangyu Wang

    (School of Built Environment, Curtin University
    Kyung Hee University)

Abstract

In this paper, a class of separable convex optimization problems with linear coupled constraints is studied. According to the Lagrangian duality, the linear coupled constraints are appended to the objective function. Then, a fast gradient-projection method is introduced to update the Lagrangian multiplier, and an inexact solution method is proposed to solve the inner problems. The advantage of our proposed method is that the inner problems can be solved in an inexact and parallel manner. The established convergence results show that our proposed algorithm still achieves optimal convergence rate even though the inner problems are solved inexactly. Finally, several numerical experiments are presented to illustrate the efficiency and effectiveness of our proposed algorithm.

Suggested Citation

  • Jueyou Li & Zhiyou Wu & Changzhi Wu & Qiang Long & Xiangyu Wang, 2016. "An Inexact Dual Fast Gradient-Projection Method for Separable Convex Optimization with Linear Coupled Constraints," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 153-171, January.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:1:d:10.1007_s10957-015-0757-1
    DOI: 10.1007/s10957-015-0757-1
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    References listed on IDEAS

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    1. Bingsheng He & Xiaoming Yuan, 2012. "An Accelerated Inexact Proximal Point Algorithm for Convex Minimization," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 536-548, August.
    2. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2011. "First-order methods of smooth convex optimization with inexact oracle," LIDAM Discussion Papers CORE 2011002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Quoc Tran Dinh & Carlo Savorgnan & Moritz Diehl, 2013. "Combining Lagrangian decomposition and excessive gap smoothing technique for solving large-scale separable convex optimization problems," Computational Optimization and Applications, Springer, vol. 55(1), pages 75-111, May.
    4. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Guoyong Gu & Bingsheng He & Junfeng Yang, 2014. "Inexact Alternating-Direction-Based Contraction Methods for Separable Linearly Constrained Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 105-129, October.
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    Cited by:

    1. Jueyou Li & Chuanye Gu & Zhiyou Wu & Changzhi Wu, 2017. "Distributed Optimization Methods for Nonconvex Problems with Inequality Constraints over Time-Varying Networks," Complexity, Hindawi, vol. 2017, pages 1-10, December.
    2. 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.
    3. Chuanye Gu & Lin Jiang & Jueyou Li & Zhiyou Wu, 2023. "Privacy-Preserving Dual Stochastic Push-Sum Algorithm for Distributed Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 22-50, April.

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