A recent proximal gradient algorithm for convex minimization problem using double inertial extrapolations

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.