Work

A Modified Three-Term Liu and Storey Derivative-Free Method for Nonlinear Monotone Equations and Applications to Signal Recovery Problems

Year: 2025

Type: article

Abstract: Iterative methods for solving nonlinear monotone equations have been developed and extensively studied. The aim of this research is to present a modified three-term Liu and Storey (TTLS) derivative-free method for nonlinear monotone equations. The proposed algorithm is derivative-free, matrix-free, and requires low storage memory; therefore, it has the capacity to solve large-scale nonlinear monotone equations. The algorithm generates a descent and a bounded search direction \(d_k\) in each iteration independent of the line search. The method is shown to be globally convergent under monotonicity and Lipschitz continuity conditions. Numerical experiments are provided to show the efficiency of the method in solving a non-linear monotone equation. Moreover, we tested the ability of the method in solving the monotone nonlinear operator equation equivalent to the \(l_1\)-norm regularized minimization problem.

Source: Thai Journal of Mathematics

Authors: Yusuf, Aliyu, Manjak, Nibron Haggai, Kwami, Abubakar Muhammad, Abdulhameed, Mohammed, Abubakar, Auwal Bala

Language: English

Topic: Iterative Methods for Nonlinear Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7217364334

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