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

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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.

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Acknowledgments

We are grateful to the anonymous referees and editor for their useful comments, which have made the paper clearer and more comprehensive than the earlier version. This work was partially supported by the Australia Research Council LP130100451, the Natural Science Foundation of China (61473326 and 11471062), the Natural Science Foundation of Chongqing (cstc2013jjB00001 and cstc2013jcyjA00029) and the Chongqing Normal University Research Foundation (15XLB005).

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Authors and Affiliations

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 400047, China

    Jueyou Li & Zhiyou Wu

  2. Australasian Joint Research Centre for Building Information Modelling, School of Built Environment, Curtin University, Perth, 6102, Australia

    Changzhi Wu & Xiangyu Wang

  3. Department of Housing and Interior Design, Kyung Hee University, Seoul, 130701, Korea

    Xiangyu Wang

  4. School of Science, Southwest University of Science and Technology, Mianyang, 621010, Sichuan, China

    Qiang Long

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  1. Jueyou Li
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  2. Zhiyou Wu
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  3. Changzhi Wu
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  4. Qiang Long
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  5. Xiangyu Wang
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Correspondence to Changzhi Wu.

Additional information

Communicated by Kok Lay Teo.

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Li, J., Wu, Z., Wu, C. et al. An Inexact Dual Fast Gradient-Projection Method for Separable Convex Optimization with Linear Coupled Constraints. J Optim Theory Appl 168, 153–171 (2016). https://doi.org/10.1007/s10957-015-0757-1

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  • DOI: https://doi.org/10.1007/s10957-015-0757-1

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