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A novel DL-type method for solving large-scale nonlinear monotone equations and compressed sensing problems

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  • Wang, Binbin
  • Wang, Xiaoliang

Abstract

In this paper, a modified Dai–Liao type conjugate gradient method is introduced for solving large-scale systems of nonlinear monotone equations with convex constraints. The approach is analyzed by minimizing the distance, under the Frobenius norm, between the search direction matrix and the scaled memoryless BFGS update matrix. The new method is a derivative-free type method, which is applicable to some large-scale optimization problems. The sufficient descent property, the global convergence property, and the linearly convergent rate are, respectively, established under mild conditions. The primary numerical results that include eight different initial points for each testing problem show the robustness of the new method. Furthermore, the method is applied to signal recovery and image reconstruction problems corrupted by salt-and-pepper impulse noise, and the results also indicate the efficiency and effectiveness of the proposed method.

Suggested Citation

  • Wang, Binbin & Wang, Xiaoliang, 2026. "A novel DL-type method for solving large-scale nonlinear monotone equations and compressed sensing problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 250(C), pages 500-523.
    • Handle: RePEc:eee:matcom:v:250:y:2026:i:c:p:500-523
    DOI: 10.1016/j.matcom.2026.07.007
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