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A Second-Order Finite-Difference Method for Derivative-Free Optimization

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  • Qian Chen
  • Peng Wang
  • Detong Zhu
  • Nan-Jing Huang

Abstract

In this paper, a second-order finite-difference method is proposed for finding the second-order stationary point of derivative-free nonconvex unconstrained optimization problems. The forward-difference or the central-difference technique is used to approximate the gradient and Hessian matrix of objective function, respectively. The traditional trust-region framework is used, and we minimize the approximation trust region subproblem to obtain the search direction. The global convergence of the algorithm is given without the fully quadratic assumption. Numerical results show the effectiveness of the algorithm using the forward-difference and central-difference approximations.

Suggested Citation

  • Qian Chen & Peng Wang & Detong Zhu & Nan-Jing Huang, 2024. "A Second-Order Finite-Difference Method for Derivative-Free Optimization," Journal of Mathematics, Hindawi, vol. 2024, pages 1-12, March.
    • Handle: RePEc:hin:jjmath:1947996
    DOI: 10.1155/2024/1947996
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    Cited by:

    1. Ana Laura Mendonça Almeida Magalhães & Pedro Paiva Brito & Geraldo Pedro da Silva Lamon & Pedro Américo Almeida Magalhães Júnior & Cristina Almeida Magalhães & Pedro Henrique Mendonça Almeida Magalhãe, 2024. "Numerical Resolution of Differential Equations Using the Finite Difference Method in the Real and Complex Domain," Mathematics, MDPI, vol. 12(12), pages 1-39, June.

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