A New Golden Ratio Inertial Algorithm with Two Types of Self Adaptive Step Sizes for Solving Nonlinear Inclusion Problems

The main purpose of this paper is to extend the golden ratio algorithm for monotone mixed variational inequalities (Math Program 184(1):383–410, 2020) to solve a nonlinear inclusion problem that involves non-monotone and locally Lipschitz continuous operators. We show that the developed iterative se...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 103; no. 3; p. 86
Main Authors: Wang, Zhong-bao, Chen, Xing-yu, Chen, Zhang-you
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2025
Springer Nature B.V
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Convergence
Inequalities
Lipschitz condition
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
Nonlinear inclusion problem
Golden ratio algorithm
Convergence and convergence rates
Inertial accelerations
Self adaptive step sizes
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:The main purpose of this paper is to extend the golden ratio algorithm for monotone mixed variational inequalities (Math Program 184(1):383–410, 2020) to solve a nonlinear inclusion problem that involves non-monotone and locally Lipschitz continuous operators. We show that the developed iterative sequence converges towards some solution of the nonlinear inclusion problem. Furthermore, our analysis reveals our algorithm owns the O ( 1 k ) convergence rate and the linear convergence rate. In addition to inheriting all the benefits of the golden ratio algorithm from (Math Program 184(1):383–410, 2020), our algorithm has inertial accelerations and two types of self adaptive step sizes, when applied to monotone mixed variational inequalities.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-025-02903-3