An efficient gradient-free projection algorithm for constrained nonlinear equations and image restoration

Abdulkarim Hassan Ibrahim; Poom Kumam; Auwal Bala Abubakar; Umar Batsari Yusuf; Seifu Endris Yimer; Kazeem Olalekan Aremu; Abdulkarim Hassan Ibrahim; Poom Kumam; Auwal Bala Abubakar; Umar Batsari Yusuf; Seifu Endris Yimer; Kazeem Olalekan Aremu

doi:10.3934/math.2021016

AIMS Mathematics

2021, Volume 6, Issue 1: 235-260. doi: 10.3934/math.2021016

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Research article

An efficient gradient-free projection algorithm for constrained nonlinear equations and image restoration

1.
KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
2.
Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
3.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4.
Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano. Kano, Nigeria
5.
Department of Mathematics and Statistics, College of Science and Technology, Hassan Usman Katsina Polytechnic, Dutsin-Ma Road, Katsina, Nigeria
6.
Department of Mathematics, College of Computation and Natural Science, Debre Berhan University, P. O. Box 445, Debre Berhan, Ethiopia
7.
Department of Mathematics, Usmanu Danfodiyo University, Sokoto 840004, Nigeria

Received: 14 July 2020 Accepted: 06 September 2020 Published: 10 October 2020
MSC : 65K05, 65L09, 90C30

Motivated by the projection technique, in this paper, we introduce a new method for approximating the solution of nonlinear equations with convex constraints. Under the assumption that the associated mapping is Lipchitz continuous and satisfies a weaker assumption of monotonicity, we establish the global convergence of the sequence generated by the proposed algorithm. Applications and numerical example are presented to illustrate the performance of the proposed method.
- unconstrained optimization,
- nonlinear equations,
- convex constrained,
- conjugate gradient method,
- projection method,
- compressive sensing
Citation: Abdulkarim Hassan Ibrahim, Poom Kumam, Auwal Bala Abubakar, Umar Batsari Yusuf, Seifu Endris Yimer, Kazeem Olalekan Aremu. An efficient gradient-free projection algorithm for constrained nonlinear equations and image restoration[J]. AIMS Mathematics, 2021, 6(1): 235-260. doi: 10.3934/math.2021016

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Abstract

Motivated by the projection technique, in this paper, we introduce a new method for approximating the solution of nonlinear equations with convex constraints. Under the assumption that the associated mapping is Lipchitz continuous and satisfies a weaker assumption of monotonicity, we establish the global convergence of the sequence generated by the proposed algorithm. Applications and numerical example are presented to illustrate the performance of the proposed method.

References

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