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Journal of Applied Mathematics and Computing

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11-01-2021 | Original Research

Solving nonlinear monotone operator equations via modified SR1 update

Authors: Auwal Bala Abubakar, Jamilu Sabi’u, Poom Kumam, Abdullah Shah

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2021

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Abstract

In this paper, we propose two algorithms for solving nonlinear monotone operator equations. The two algorithms are based on the conjugate gradient method. The corresponding search directions were obtained via a modified memoryless symmetric rank-one (SR1) update. Independent of the line search, the two directions were shown to be sufficiently descent and bounded. Moreover, the convergence of the algorithms were established under suitable assumptions on the operator under consideration. In addition, numerical experiments were conducted on some benchmark test problems to depict the efficiency and competitiveness of the algorithms compared with existing algorithms. From the results of the experiments, we can conclude that the proposed algorithms are more efficient and robust.

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Title: Solving nonlinear monotone operator equations via modified SR1 update
Authors: Auwal Bala Abubakar
Jamilu Sabi’u
Poom Kumam
Abdullah Shah
Publication date: 11-01-2021
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2021
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-020-01461-1

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