A MODIﬁED SELF-ADAPTIVE CONJUGATE GRADIENT METHOD FOR SOLVING CONVEX CONSTRAINED MONOTONE NONLINEAR EQUATIONS WITH APPLICATIONS TO SIGNAL RECOVERY PROBLEMS

Auwal Bala Abubakar; Poom Kumam; Aliyu Muhammed Awwal

A MODIﬁED SELF-ADAPTIVE CONJUGATE GRADIENT METHOD FOR SOLVING CONVEX CONSTRAINED MONOTONE NONLINEAR EQUATIONS WITH APPLICATIONS TO SIGNAL RECOVERY PROBLEMS

Authors

Auwal Bala Abubakar Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano. Kano, Nigeria
Poom Kumam KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 26 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Aliyu Muhammed Awwal Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria

Keywords:

Non-linear equations, Conjugate gradient method, Projection method, Convex constraints, Signal reconstruction problem

Abstract

In this article, we propose a modiﬁed self-adaptive conjugate gradient algorithm for handling nonlinear monotone equations with the constraints being convex. Under some nice conditions, the global convergence of the method was established. Numerical examples reported show that the method is promising and eﬃcient for solving monotone nonlinear equations. In addition, we applied the proposed algorithm to solve sparse signal reconstruction problems.

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Published

2019-12-31

How to Cite

Abubakar, A. B., Kumam, P., & Awwal, A. M. (2019). A MODIﬁED SELF-ADAPTIVE CONJUGATE GRADIENT METHOD FOR SOLVING CONVEX CONSTRAINED MONOTONE NONLINEAR EQUATIONS WITH APPLICATIONS TO SIGNAL RECOVERY PROBLEMS. Bangmod International Journal of Mathematical and Computational Science, 5, 1–26. Retrieved from https://bangmodjmcs.com/index.php/bangmodmcs/article/view/41