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A unified derivative-free projection method model for large-scale nonlinear equations with convex constraints

  • * Corresponding author: Yigui Ou

    * Corresponding author: Yigui Ou 

Supported by NNSF of China (No. 11961018), NSF of Hainan Province (No. 120QN175) and Innovative Project for Postgraduates of Hainan Province (No. Hys2020-107)

Abstract Full Text(HTML) Figure(4) / Table(1) Related Papers Cited by
  • Motivated by recent derivative-free projection methods proposed in the literature for solving nonlinear constrained equations, in this paper we propose a unified derivative-free projection method model for large-scale nonlinear equations with convex constraints. Under mild conditions, the global convergence and convergence rate of the proposed method are established. In order to verify the feasibility and effectiveness of the model, a practical algorithm is devised and the corresponding numerical experiments are reported, which show that the proposed practical method is efficient and can be applied to solve large-scale nonsmooth equations. Moreover, the proposed practical algorithm is also extended to solve the obstacle problem.

    Mathematics Subject Classification: Primary: 90C25, 65H10; Secondary: 65K05.


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  • Figure 1.  Performance profile for the number of iterations

    Figure 2.  Performance profile for the number of function evaluations

    Figure 3.  Performance profile for the CPU time

    Figure 4.  An elastic string stretched over an obstacle

    Table 1.  Numerical test results for the obstale problem

    n Algorithm5.1 OLA (CPU/FN) XZA (CPU/FN)
    50 1.664626/9.7218e-06 1.814302/7.1023e-06 4.972539/9.9601e-06
    100 10.632101/5.9094e-05 10.647692/8.0831e-05 39.520620/1.3001e-05
    500 90.768111/0.0161 167.333069/0.0174 459.419363/0.0279
     | Show Table
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