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New inertial forward–backward algorithm for convex minimization with applications

Kankam Kunrada, Cholamjiak Watcharaporn, Cholamjiak Prasit

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20220188

In this work, we present a new proximal gradient algorithm based on Tseng’s extragradient method and an inertial technique to solve the convex minimization problem in real Hilbert spaces. Using the stepsize rules, the selection of the Lipschitz constant of the gradient of functions is avoided. We then prove the weak convergence theorem and present the numerical experiments for image recovery. The comparative results show that the proposed algorithm has better efficiency than other methods.