An inertial forward-backward splitting method for approximating solutions of certain optimization problems

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

doi:10.23952/jnfa.2020.6

An inertial forward-backward splitting method for approximating solutions of certain optimization problems

H. A. Abass, K. O. Aremu, L. O. Jolaoso, O. T. Mewomo^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

59 Citations (Scopus)

Abstract

The purpose of this paper is to introduce an inertial-type iterative algorithm for approximating solutions of a split general system of variational inequalities, minimization problems and fixed point problems of a finite family of quasi-nonexpansive mappings. We prove a strong convergence theorem in the framework of real Hilbert spaces. An application to split feasibility problems is also presented. A numerical example is provided to show the applicability of our main results.

Original language	English
Article number	6
Journal	Journal of Nonlinear Functional Analysis
Volume	2020
DOIs	https://doi.org/10.23952/jnfa.2020.6
Publication status	Published - 2020
Externally published	Yes

Keywords

Fixed point problem
Inertial iterative scheme
Minimization problem
Split general system of variational inequalities

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10.23952/jnfa.2020.6

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abstract = "The purpose of this paper is to introduce an inertial-type iterative algorithm for approximating solutions of a split general system of variational inequalities, minimization problems and fixed point problems of a finite family of quasi-nonexpansive mappings. We prove a strong convergence theorem in the framework of real Hilbert spaces. An application to split feasibility problems is also presented. A numerical example is provided to show the applicability of our main results.",

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AU - Aremu, K. O.

AU - Jolaoso, L. O.

AU - Mewomo, O. T.

PY - 2020

Y1 - 2020

N2 - The purpose of this paper is to introduce an inertial-type iterative algorithm for approximating solutions of a split general system of variational inequalities, minimization problems and fixed point problems of a finite family of quasi-nonexpansive mappings. We prove a strong convergence theorem in the framework of real Hilbert spaces. An application to split feasibility problems is also presented. A numerical example is provided to show the applicability of our main results.

AB - The purpose of this paper is to introduce an inertial-type iterative algorithm for approximating solutions of a split general system of variational inequalities, minimization problems and fixed point problems of a finite family of quasi-nonexpansive mappings. We prove a strong convergence theorem in the framework of real Hilbert spaces. An application to split feasibility problems is also presented. A numerical example is provided to show the applicability of our main results.

KW - Fixed point problem

KW - Inertial iterative scheme

KW - Minimization problem

KW - Split general system of variational inequalities

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JO - Journal of Nonlinear Functional Analysis

JF - Journal of Nonlinear Functional Analysis

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An inertial forward-backward splitting method for approximating solutions of certain optimization problems

Abstract

Keywords

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