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An improved first-order primal-dual algorithm with a new correction step

Author

Listed:
  • Xingju Cai
  • Deren Han
  • Lingling Xu

Abstract

In this paper, we propose a new correction strategy for some first-order primal-dual algorithms arising from solving, e.g., total variation image restoration. With this strategy, we can prove the convergence of the algorithm under more flexible conditions than those proposed most recently. Some preliminary numerical results of image deblurring support that the new correction strategy can improve the numerical efficiency. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Xingju Cai & Deren Han & Lingling Xu, 2013. "An improved first-order primal-dual algorithm with a new correction step," Journal of Global Optimization, Springer, vol. 57(4), pages 1419-1428, December.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:4:p:1419-1428
    DOI: 10.1007/s10898-012-9999-8
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    Cited by:

    1. Ying Gao & Wenxing Zhang, 2023. "An alternative extrapolation scheme of PDHGM for saddle point problem with nonlinear function," Computational Optimization and Applications, Springer, vol. 85(1), pages 263-291, May.
    2. Yu, Yongchao & Peng, Jigen, 2018. "A modified primal-dual method with applications to some sparse recovery problems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 76-94.
    3. Hongjin He & Jitamitra Desai & Kai Wang, 2016. "A primal–dual prediction–correction algorithm for saddle point optimization," Journal of Global Optimization, Springer, vol. 66(3), pages 573-583, November.
    4. Fan Jiang & Zhiyuan Zhang & Hongjin He, 2023. "Solving saddle point problems: a landscape of primal-dual algorithm with larger stepsizes," Journal of Global Optimization, Springer, vol. 85(4), pages 821-846, April.

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