Enhanced Projection Method for the Solution of the System of Nonlinear Equations Under a More General Assumption than Pseudo-Monotonicity and Lipschitz Continuity

Kanikar Muangchoo and Auwal Bala Abubakar ()
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Kanikar Muangchoo: Department of Mathematics and Statistics, Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon (RMUTP), 1381 Pracharat 1 Road, Wongsawang, Bang Sue, Bangkok 10800, Thailand
Auwal Bala Abubakar: Department of Art and Science, George Mason University, Songdomunhwa-ro 119-4, Yeonsu-gu, Incheon 21985, Republic of Korea

Mathematics, 2024, vol. 12, issue 23, 1-17

Abstract: In this manuscript, we propose an efficient algorithm for solving a class of nonlinear operator equations. The algorithm is an improved version of previously established method. The algorithm’s features are as follows: (i) the search direction is bounded and satisfies the sufficient descent condition; (ii) the global convergence is achieved when the operator is continuous and satisfies a condition weaker than pseudo-monotonicity. Moreover, by comparing it with previously established method the algorithm’s efficiency was shown. The comparison was based on the iteration number required for each algorithm to solve a particular problem and the time taken. Some benchmark test problems, which included monotone and pseudo-monotone problems, were considered for the experiments. Lastly, the algorithm was utilized to solve the logistic regression (prediction) model.

Keywords: iterative methods; pseudo-monotone nonlinear equations; conjugate gradient method; logistic regression (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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