Strongly convergent doubly accelerated forward-backward algorithm for monotone inclusion and fixed point problems

Abstract

In this paper, we study the development of efficient iterative algorithm for finding a common solution to monotone inclusion problems and fixed point problems in real Hilbert spaces. These problems arise naturally in optimization, equilibrium modeling, signal processing, and other applied fields. We propose a doubly accelerated forward-backward algorithm with a viscosity term, combining inertial techniques and extragradient steps to enhance convergence speed and stability. The proposed algorithm relaxes restrictive assumptions on the underlying operators and guarantees strong convergence under mild conditions. Extensive numerical experiments illustrate the effectiveness and superiority of our method compared to existing approaches.