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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/1947996 |
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| _version_ | 1841524294238076928 |
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| author | Qian Chen Peng Wang Detong Zhu |
| author_facet | Qian Chen Peng Wang Detong Zhu |
| author_sort | Qian Chen |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-adb82fc6b039402db930f2224a5873a5 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-adb82fc6b039402db930f2224a5873a52025-02-03T07:23:24ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/1947996A Second-Order Finite-Difference Method for Derivative-Free OptimizationQian Chen0Peng Wang1Detong Zhu2Mathematics and Statistics CollegeMathematics and Statistics CollegeMathematics and Science CollegeIn 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.http://dx.doi.org/10.1155/2024/1947996 |
| spellingShingle | Qian Chen Peng Wang Detong Zhu A Second-Order Finite-Difference Method for Derivative-Free Optimization Journal of Mathematics |
| title | A Second-Order Finite-Difference Method for Derivative-Free Optimization |
| title_full | A Second-Order Finite-Difference Method for Derivative-Free Optimization |
| title_fullStr | A Second-Order Finite-Difference Method for Derivative-Free Optimization |
| title_full_unstemmed | A Second-Order Finite-Difference Method for Derivative-Free Optimization |
| title_short | A Second-Order Finite-Difference Method for Derivative-Free Optimization |
| title_sort | second order finite difference method for derivative free optimization |
| url | http://dx.doi.org/10.1155/2024/1947996 |
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