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A primal–dual prediction–correction algorithm for saddle point optimization

Author

Listed:
  • Hongjin He

    (Hangzhou Dianzi University)

  • Jitamitra Desai

    (Nanyang Technological University)

  • Kai Wang

    (Nanyang Technological University)

Abstract

In this paper, we introduce a new primal–dual prediction–correction algorithm for solving a saddle point optimization problem, which serves as a bridge between the algorithms proposed in Cai et al. (J Glob Optim 57:1419–1428, 2013) and He and Yuan (SIAM J Imaging Sci 5:119–149, 2012). An interesting byproduct of the proposed method is that we obtain an easily implementable projection-based primal–dual algorithm, when the primal and dual variables belong to simple convex sets. Moreover, we establish the worst-case $${\mathcal {O}}(1/t)$$ O ( 1 / t ) convergence rate result in an ergodic sense, where t represents the number of iterations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:66:y:2016:i:3:d:10.1007_s10898-016-0437-1
    DOI: 10.1007/s10898-016-0437-1
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    References listed on IDEAS

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    1. 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.
    2. Guoyong Gu & Bingsheng He & Xiaoming Yuan, 2014. "Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: a unified approach," Computational Optimization and Applications, Springer, vol. 59(1), pages 135-161, October.
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    Cited by:

    1. 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.
    2. 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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