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<p>This paper presents a novel class of forward-backward algorithms designed to solve convex minimization problems by incorporating a self-adaptive step-size mechanism and multiple inertial extrapolation terms. Under appropriate conditions on the algorithmic parameters, both weak and strong convergence theorems are established, confirming the theoretical robustness of the proposed methods. The practical performance is validated through three numerical experiments: an infinite-dimensional example, an image inpainting task, and a data classification problem related to oral cancer diagnosis. The proposed algorithm achieves superior results in terms of PSNR and SSIM for image restoration and demonstrates high accuracy in medical image classification, using an augmented dataset expanded from 950 to 10,790 images. Overall, the findings highlight the effectiveness of the proposed algorithms, making them highly applicable to real-world inverse problems and data-driven tasks in medical and imaging sciences.</p>

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Enhanced proximal gradient methods with multi inertial terms for minimization problem

  • 期刊论文

  • 发表日期：

    2025年8月5日

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  • Kunrada Kankam,
  • Watcharaporn Cholamjiak,
  • Prasit Cholamjiak,
  • Jen-Chih Yao

摘要

This paper presents a novel class of forward-backward algorithms designed to solve convex minimization problems by incorporating a self-adaptive step-size mechanism and multiple inertial extrapolation terms. Under appropriate conditions on the algorithmic parameters, both weak and strong convergence theorems are established, confirming the theoretical robustness of the proposed methods. The practical performance is validated through three numerical experiments: an infinite-dimensional example, an image inpainting task, and a data classification problem related to oral cancer diagnosis. The proposed algorithm achieves superior results in terms of PSNR and SSIM for image restoration and demonstrates high accuracy in medical image classification, using an augmented dataset expanded from 950 to 10,790 images. Overall, the findings highlight the effectiveness of the proposed algorithms, making them highly applicable to real-world inverse problems and data-driven tasks in medical and imaging sciences.