An Inertial Three-term Derivative-free Projection Algorithm for Nonlinear Equations without Pseudo-monotonicity

Xiaoyu Wu (), Hu Shao (), Pengjie Liu () and Feng Shao ()
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Xiaoyu Wu: Jiangsu Center for Applied Mathematics, China University of Mining and Technology
Hu Shao: Jiangsu Center for Applied Mathematics, China University of Mining and Technology
Pengjie Liu: Jiangsu Center for Applied Mathematics, China University of Mining and Technology
Feng Shao: Jiangsu Center for Applied Mathematics, China University of Mining and Technology

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 2, No 17, 30 pages

Abstract: Abstract In this paper, we focus on developing a general form of inertial iterative method for the system of unconstrained nonlinear equations, which has extensive and practical applications. Combining the inertial step and projection technique, a family of three-term conjugate gradient projection method is proposed for finding the approximate solution of nonlinear equations. The search direction is modified based on the scaled memoryless BFGS formula, satisfying the sufficient descent property. Our methods are suitable for large-scale equations since they are low storage memory and derivative-free. Moreover, we analyze the global convergence of the proposed method without the monotonicity or pseudo-monotonicity as well as the Lipschitz continuity hypothesis of the system of nonlinear equations. Additionally, the numerical experiments on nonlinear equations and applications on compressed sensing problems are conducted to verify the effectiveness of our methods.

Keywords: System of unconstrained nonlinear equations; Derivative-free projection algorithm; Inertial step; Global convergence; Image restoration; 65K05; 90C56 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02711-7

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