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mmr 2022, 8(1): 1-18 |
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Ahmadvand M, Esmaeilbeigi M, Kamandi A, Mohammadi Yaghoobi F. A new trust-region algorithm based on radial basis function interpolation. mmr 2022; 8 (1) :1-18
URL: http://mmr.khu.ac.ir/article-1-2886-en.html
URL: http://mmr.khu.ac.ir/article-1-2886-en.html
1- Islamic Azad University Malayer branch , mohammad_ahmadvand@yahoo.com
2- Malayer University
3- University of Science and Technology of Mazandaran
4- Hamedan Branch, Islamic Azad University
2- Malayer University
3- University of Science and Technology of Mazandaran
4- Hamedan Branch, Islamic Azad University
Abstract: (1218 Views)
Optimization using radial basis functions as an interpolation tool in trust-region (ORBIT), is a derivative-free framework based on fully linear models to solve unconstrained local optimization, especially when the function evaluations are computationally expensive. This algorithm stores the interpolation points and function values to using at subsequent iterations. Despite the comparatively advanced management used for interpolation points, we maintain that ORBIT ignores sorting the interpolation points based on the function values. In this paper, we propose an improved version SORT-ORBIT by sorting the interpolation points and selecting a point as the trust-region center in which the objective function reaches its minimum value. Numerical results indicate the efficiency of the improved version compared with the original version. In addition, to estimate high-accuracy solutions, we equip the ORBIT with a new gradient-free convergence test.
Keywords: Trust-region algorithm, Radial basis function, Unconstrained optimization, Derivative-free algorithm, Center changing, Convergence test.
Type of Study: S |
Subject:
alg
Received: 2018/12/6 | Revised: 2022/11/15 | Accepted: 2020/07/13 | Published: 2022/05/14 | ePublished: 2022/05/14
Received: 2018/12/6 | Revised: 2022/11/15 | Accepted: 2020/07/13 | Published: 2022/05/14 | ePublished: 2022/05/14
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