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

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 obje...

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Published in:Journal of mathematics (Hidawi) 2024, Vol.2024, p.1-12
Main Authors: Chen, Qian, Wang, Peng, Zhu, Detong
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Convex analysis
Finite difference method
Hessian matrices
Mathematical analysis
Methods
Optimization
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description 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.
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subjects Algorithms
Approximation
Convex analysis
Finite difference method
Hessian matrices
Mathematical analysis
Methods
Optimization
title A Second-Order Finite-Difference Method for Derivative-Free Optimization
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