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An Accelerated Inexact Proximal Point Algorithm for Convex Minimization

Author

Listed:
  • Bingsheng He

    (Nanjing University)

  • Xiaoming Yuan

    (Hong Kong Baptist University)

Abstract

The proximal point algorithm is classical and popular in the community of optimization. In practice, inexact proximal point algorithms which solve the involved proximal subproblems approximately subject to certain inexact criteria are truly implementable. In this paper, we first propose an inexact proximal point algorithm with a new inexact criterion for solving convex minimization, and show its O(1/k) iteration-complexity. Then we show that this inexact proximal point algorithm is eligible for being accelerated by some influential acceleration schemes proposed by Nesterov. Accordingly, an accelerated inexact proximal point algorithm with an iteration-complexity of O(1/k 2) is proposed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:2:d:10.1007_s10957-011-9948-6
    DOI: 10.1007/s10957-011-9948-6
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    Cited by:

    1. Julian Rasch & Antonin Chambolle, 2020. "Inexact first-order primal–dual algorithms," Computational Optimization and Applications, Springer, vol. 76(2), pages 381-430, June.
    2. Myeongmin Kang & Myungjoo Kang & Miyoun Jung, 2015. "Inexact accelerated augmented Lagrangian methods," Computational Optimization and Applications, Springer, vol. 62(2), pages 373-404, November.
    3. 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.

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