ISSN:2582-5208

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Paper Key : IRJ************676
Author: Alaa Luqman Ibrahim,Mohammed Guhdar Mohammed
Date Published: 13 Jan 2023
Abstract
The Quasi-Newton (QN) method is a widely used stationary iterative method for solving unconstrained optimization problems. One particular method within the Quasi-Newton family is the Symmetric Rank-One (SR1) method. In this research, we propose a new variant of the Quasi-Newton SR1 method that utilizes the Barzilai-Borwein step size. Our analysis demonstrates that the updated matrix resulting from the proposed method is both symmetric and positive definite. Additionally, our numerical experiments show that the proposed SR1 method, when combined with the PCG method, is effective in solving unconstrained optimization problems, as evidenced by its low number of iterations and function evaluations. Furthermore, we demonstrate that our proposed SR1 method is more efficient in solving large-scale problems with a varying number of variables compared to the original method. The numerical results of applying the new SR1 method to neural network problems also reveal its effectiveness.
DOI LINK : 10.56726/IRJMETS32949 https://www.doi.org/10.56726/IRJMETS32949
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