A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications

Charles E Chidume,Poom Kumam,Abubakar Adamu

doi:10.1186/s13663-020-00678-w

Abstract

An inertial iterative algorithm for approximating a point in the set of zeros of a maximal monotone operator which is also a common fixed point of a countable family of relatively nonexpansive operators is studied. Strong convergence theorem is proved in a uniformly convex and uniformly smooth real Banach space. This theorem extends, generalizes and complements several recent important results. Furthermore, the theorem is applied to convex optimization problems and to J-fixed point problems. Finally, some numerical examples are presented to show the effect of the inertial term in the convergence of the sequence of the algorithm.

Highlights

An inertial-type algorithm was first introduced and studied by Polyak [35], as a method of speeding up the convergence of the sequence of an algorithm
Numerical experiments have shown that an algorithm with an inertial extrapolation term converges faster than an algorithm without it
T is called monotone if p – q, p∗ – q∗ ≥ 0, ∀p∗ ∈ Tp, q∗ ∈ Tq

Summary

Introduction

An inertial-type algorithm was first introduced and studied by Polyak [35], as a method of speeding up the convergence of the sequence of an algorithm. In 2018, Chidume et al [12] introduced and studied an inertial-type algorithm in a uniformly convex and uniformly smooth real Banach space.

Results

Conclusion