A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space

Abstract

In this paper, we study the strong convergence of the proximal gradient algorithm with inertial extrapolation term for solving classical minimization problem and finding the fixed points of $\delta $-demimetric mapping in a real Hilbert space. Our algorithm is inspired by the inertial proximal point algorithm and the viscosity approximation method of Moudafi. A strong convergence result is achieved in our result without necessarily imposing the summation condition $\sum _{n=1}^\infty \beta _n\Vert x_{n-1} -x_n\Vert < + \infty $ on the inertial term. Finally, we provide some applications and numerical example to show the efficiency and accuracy of our algorithm. Our results improve and complement many other related results in the literature.