数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (3): 1462-1476.doi: 10.1007/s10473-023-0326-x

• • 上一篇    

DOUBLE INERTIAL PROXIMAL GRADIENT ALGORITHMS FOR CONVEX OPTIMIZATION PROBLEMS AND APPLICATIONS*

Kunrada Kankam, Prasit Cholamjiak   

  1. School of Science, University of Phayao, Phayao 56000, Thailand
  • 收稿日期:2022-04-06 修回日期:2022-08-25 出版日期:2023-06-25 发布日期:2023-06-06
  • 通讯作者: Prasit Cholamjiak, E-mail: prasitch2008@yahoo.com
  • 作者简介:Kunrada Kankam, E-mail: kunradazzz@gmail.com
  • 基金资助:
    National Research Council of Thailand (NRCT) under grant no. N41A640094 and the Thailand Science Research and Innovation Fund and the University of Phayao under the project FF66-UoE.

DOUBLE INERTIAL PROXIMAL GRADIENT ALGORITHMS FOR CONVEX OPTIMIZATION PROBLEMS AND APPLICATIONS*

Kunrada Kankam, Prasit Cholamjiak   

  1. School of Science, University of Phayao, Phayao 56000, Thailand
  • Received:2022-04-06 Revised:2022-08-25 Online:2023-06-25 Published:2023-06-06
  • Contact: Prasit Cholamjiak, E-mail: prasitch2008@yahoo.com
  • About author:Kunrada Kankam, E-mail: kunradazzz@gmail.com
  • Supported by:
    National Research Council of Thailand (NRCT) under grant no. N41A640094 and the Thailand Science Research and Innovation Fund and the University of Phayao under the project FF66-UoE.

摘要: In this paper, we propose double inertial forward-backward algorithms for solving unconstrained minimization problems and projected double inertial forward-backward algorithms for solving constrained minimization problems. We then prove convergence theorems under mild conditions. Finally, we provide numerical experiments on image restoration problem and image inpainting problem. The numerical results show that the proposed algorithms have more efficient than known algorithms introduced in the literature.

关键词: weak convergence, forward-backward algorithm, convex minimization, inertial technique

Abstract: In this paper, we propose double inertial forward-backward algorithms for solving unconstrained minimization problems and projected double inertial forward-backward algorithms for solving constrained minimization problems. We then prove convergence theorems under mild conditions. Finally, we provide numerical experiments on image restoration problem and image inpainting problem. The numerical results show that the proposed algorithms have more efficient than known algorithms introduced in the literature.

Key words: weak convergence, forward-backward algorithm, convex minimization, inertial technique