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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年5月27日

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  • Xiaoyu Wu,
  • Hu Shao,
  • Pengjie Liu,
  • Feng Shao

摘要

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.