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<p>This article proposes and analyzes a family of derivative-free projection methods, incorporating a two-step inertial technique, for solving large-scale nonlinear pseudo-monotone equations with convex constraints. The search directions generated by the proposed method offer great flexibility in selecting <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\beta_k\)</EquationSource> </InlineEquation> and incorporate more information about the objective function. These directions also satisfy the sufficient descent property and are independent of any line search rules. Moreover, under the assumption of local Lipschitz continuity, we establish asymptotic and non-asymptotic global convergence rates. Numerical results show the efficiency of the proposed method. Finally, the proposed method is applied to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\ell_2\)</EquationSource> </InlineEquation>-regularized logistic regression and sparse signal restoration, demonstrating efficacy in real-world applications.</p>

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A family of derivative-free projection methods with the modified two-step inertial strategy for constrained nonlinear pseudo-monotone equations

  • 期刊论文

  • 发表日期：

    2026年1月3日

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  • Guodong Ma,
  • Junji Wang,
  • Jinbao Jian,
  • Wei Zhang,
  • Xiang Luo

摘要

This article proposes and analyzes a family of derivative-free projection methods, incorporating a two-step inertial technique, for solving large-scale nonlinear pseudo-monotone equations with convex constraints. The search directions generated by the proposed method offer great flexibility in selecting \(\beta_k\) and incorporate more information about the objective function. These directions also satisfy the sufficient descent property and are independent of any line search rules. Moreover, under the assumption of local Lipschitz continuity, we establish asymptotic and non-asymptotic global convergence rates. Numerical results show the efficiency of the proposed method. Finally, the proposed method is applied to \(\ell_2\) -regularized logistic regression and sparse signal restoration, demonstrating efficacy in real-world applications.