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Improvement of the Nelder-Mead method using Direct Inversion in Iterative Subspace
- Source :
- Optimization and Engineering. 23:1033-1055
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- The Nelder-Mead (NM) method is a popular derivative-free optimization algorithm owing to its fast convergence and robustness. However, it is known that the method often fails to converge or costs a long time for a large-scale optimization. In the present study, the NM method has been improved using direct inversion in iterative subspace (DIIS). DIIS is a technique to accelerate an optimization method, extrapolating a better intermediate solution from linear-combination of the known ones. We compared runtimes of the new method (NM-DIIS) and the conventional NM method using unimodal test functions with various dimensions. The NM-DIIS method showed better results than the original NM on average when the dimension of the objective function is high. Long tails of the runtime distributions in the NM method have disappeared when DIIS was applied. DIIS has also been implemented in the quasi-gradient method, which is an improved version of the NM method developed by Pham et al. [IEEE Trans. Ind. Informatics, 7 (2011) 592]. The combined method also performed well especially in an upwardly convex test function. The present study proposes a practical optimization strategy and proves the versatility of DIIS.
- Subjects :
- 021103 operations research
Control and Optimization
Computer science
Mechanical Engineering
0211 other engineering and technologies
Regular polygon
Aerospace Engineering
02 engineering and technology
DIIS
Dimension (vector space)
Robustness (computer science)
Convergence (routing)
Test functions for optimization
021108 energy
Electrical and Electronic Engineering
Nelder–Mead method
Algorithm
Software
Subspace topology
Civil and Structural Engineering
Subjects
Details
- ISSN :
- 15732924 and 13894420
- Volume :
- 23
- Database :
- OpenAIRE
- Journal :
- Optimization and Engineering
- Accession number :
- edsair.doi...........1b6a0eea256802481b20f3c297facb67