@article{Kesornprom2024, 
author = {Suparat Kesornprom and Papatsara Inkrong and Uamporn Witthayarat and Prasit Cholamjiak},
title = {A recent proximal gradient algorithm for convex minimization problem using double inertial extrapolations},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {18841-18859},
keywords = {forward-backward algorithm, minimization problem, inertial extrapolation, weak convergence},
url = {https://www.sciopen.com/article/10.3934/math.2024917},
doi = {10.3934/math.2024917},
abstract = {In this study, we suggest a new class of forward-backward (FB) algorithms designed to solve convex minimization problems. Our method incorporates a linesearch technique, eliminating the need to choose Lipschitz assumptions explicitly. Additionally, we apply double inertial extrapolations to enhance the algorithm's convergence rate. We establish a weak convergence theorem under some mild conditions. Furthermore, we perform numerical tests, and apply the algorithm to image restoration and data classification as a practical application. The experimental results show our approach's superior performance and effectiveness, surpassing some existing methods in the literature.}
}