An alternating inertial forward-backward-forward algorithm for solving monotone inclusion problem and its applications

We present an alternating inertial forward-backward-forward algorithm designed to find the zeros of the sum of a maximally monotone operator and a single-valued monotone operator that is also Lipschitz continuous. This study aims to extend Tseng’s forward-backward-forward algorithm by incorporating alternating inertial effects. We then apply our enhanced algorithm to address convex minimization problems. Key topics include the monotone inclusion problem, forward-backward-forward algorithm, the alternating inertial method, and convex minimization problems. Lastly, we explore the application of our proposed approach in image restoration, emphasizing its effectiveness and adaptability.