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<p>In this paper, based on the two-step inertial technique and the modified Hager-Zhang conjugate gradient method, we present a two-step inertial Hager-Zhang derivative-free projection method with an adaptive line search for solving nonlinear equations. The search direction generated by the proposed method possesses certain nice properties independent of line searches. The global convergence is established without both the Lipschitz continuity condition and the pseudo-monotonicity of the underlying mapping. Importantly, under the local Lipschitz continuity condition, we establish the asymptotic convergence rate of the proposed method and show the iteration-complexity bound for finding an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\epsilon \)</EquationSource> </InlineEquation>-approximation solution with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\epsilon &gt;0\)</EquationSource> </InlineEquation>. To the best of our knowledge, these theoretical results obtained are new compared with existing relevant algorithms in the literature. Finally, numerical results indicate the efficiency of the proposed method in solving standard nonlinear equations and sparse signal restoration problems.</p>

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A two-step inertial Hager-Zhang derivative-free projection method for solving nonlinear equations with applications

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Jinbao Jian,
  • Ziyu Li,
  • Jianghua Yin,
  • Xianzhen Jiang,
  • Hongxue Shen

摘要

In this paper, based on the two-step inertial technique and the modified Hager-Zhang conjugate gradient method, we present a two-step inertial Hager-Zhang derivative-free projection method with an adaptive line search for solving nonlinear equations. The search direction generated by the proposed method possesses certain nice properties independent of line searches. The global convergence is established without both the Lipschitz continuity condition and the pseudo-monotonicity of the underlying mapping. Importantly, under the local Lipschitz continuity condition, we establish the asymptotic convergence rate of the proposed method and show the iteration-complexity bound for finding an \(\epsilon \) -approximation solution with \(\epsilon >0\) . To the best of our knowledge, these theoretical results obtained are new compared with existing relevant algorithms in the literature. Finally, numerical results indicate the efficiency of the proposed method in solving standard nonlinear equations and sparse signal restoration problems.