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

L.O. Jolaoso; H.A. Abass; O.T. Mewomo

Archivum Mathematicum (2019)

  • Volume: 055, Issue: 3, page 167-194
  • ISSN: 0044-8753

Abstract

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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 δ -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 ∑ n = 1 ∞ β n ∥ x n - 1 - x n ∥ < + ∞ 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.

How to cite

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Jolaoso, L.O., Abass, H.A., and Mewomo, O.T.. "A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space." Archivum Mathematicum 055.3 (2019): 167-194. <http://eudml.org/doc/294843>.

@article{Jolaoso2019,
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.},
author = {Jolaoso, L.O., Abass, H.A., Mewomo, O.T.},
journal = {Archivum Mathematicum},
keywords = {proximal gradient algorithm; proximal operator; demimetric mappings; inertial algorithm; viscosity approximation; Meir Keeler contraction; fixed point theory},
language = {eng},
number = {3},
pages = {167-194},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space},
url = {http://eudml.org/doc/294843},
volume = {055},
year = {2019},
}

TY - JOUR
AU - Jolaoso, L.O.
AU - Abass, H.A.
AU - Mewomo, O.T.
TI - A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space
JO - Archivum Mathematicum
PY - 2019
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 055
IS - 3
SP - 167
EP - 194
AB - 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.
LA - eng
KW - proximal gradient algorithm; proximal operator; demimetric mappings; inertial algorithm; viscosity approximation; Meir Keeler contraction; fixed point theory
UR - http://eudml.org/doc/294843
ER -

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