Forward-Backward Splitting Method with Viscosity Iteration for Solving Monotone Inclusion Problems

• Author(s): Francis O Nwawuru; Grace N Echezona
• Paper ID: 1704279
• Page: 588-594
• Published Date: 27-04-2023
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 6 Issue 10 April-2023

Abstract

In this paper, we introduce and study a modified forward-backward splitting method for finding a zero inthe sum of two monotone operators in real Hilbert spaces. Our proposed method only requires one forward evaluation of the single-valued operator and onebackward evaluation of the set-valued operator per iteration. This is an improvement over many others in literature with strongly convergent splitting methods with two forwards and a backward iteration. Furthermore, we also incorporate inertial term in our scheme to speed up the rate of convergence. We obtain a strong convergence result when the set-valued operator is maximal monotoneand the single-valued operator is Lipschitz continuous monotone which is weaker assumption than being inverse strongly monotone or cocoercive.

Keywords

viscosity iteration method; Inertial method; Inclusion problem; Maximal monotone operator; Forward?backward algorithm.

Citations

IRE Journals:
Francis O Nwawuru, Grace N Echezona "Forward-Backward Splitting Method with Viscosity Iteration for Solving Monotone Inclusion Problems" Iconic Research And Engineering Journals Volume 6 Issue 10 2023 Page 588-594

IEEE:
Francis O Nwawuru, Grace N Echezona "Forward-Backward Splitting Method with Viscosity Iteration for Solving Monotone Inclusion Problems" Iconic Research And Engineering Journals, vol. 6, no. 10, Apr. 2023

APA:
Francis O Nwawuru, Grace N Echezona (2023). Forward-Backward Splitting Method with Viscosity Iteration for Solving Monotone Inclusion Problems. Iconic Research And Engineering Journals, 6(10).

MLA:
Francis O Nwawuru, Grace N Echezona "Forward-Backward Splitting Method with Viscosity Iteration for Solving Monotone Inclusion Problems" Iconic Research And Engineering Journals, vol. 6, no. 10, Apr. 2023.

BibTeX

@article{1704279,
author = {Francis O Nwawuru, Grace N Echezona},
title = {Forward-Backward Splitting Method with Viscosity Iteration for Solving Monotone Inclusion Problems},
journal = {Iconic Research And Engineering Journals},
year = {2023},
volume = {6},
number = {10},
pages = {588-594},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1704279.pdf},
abstract = {In this paper, we introduce and study a modified forward-backward splitting method for finding a zero inthe sum of two monotone operators in real Hilbert spaces. Our proposed method only requires one forward evaluation of the single-valued operator and onebackward evaluation of the set-valued operator per iteration. This is an improvement over many others in literature with strongly convergent splitting methods with two forwards and a backward iteration. Furthermore, we also incorporate inertial term in our scheme to speed up the rate of convergence. We obtain a strong convergence result when the set-valued operator is maximal monotoneand the single-valued operator is Lipschitz continuous monotone which is weaker assumption than being inverse strongly monotone or cocoercive.},
keywords = {viscosity iteration method; Inertial method; Inclusion problem; Maximal monotone operator; Forward?backward algorithm.},
month = {April}
}