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Using complex step numerical differentiation in the Broyden-Fletcher-Goldfard-Shanno algorithm Chen, Jinghong
Abstract
We conduct a study on an alternative method to Derivative-Free Optimization (DFO). It is a method by applying numerical differentiation techniques to the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. We apply different gradient approximation strategies on the BFGS, particularly a complex-step method to the gradient approximation. We conduct an experiment to test the feasibility of the approximation-based-BFGS methods. The experiment also explores the efficiency and reliability of BFGS algorithm with different strategies and different settings. Results find that the approximation-based-BFGS method is feasible alternative to DFO. With appropriate parameter settings, approximation-based-BFGS methods achieve high level accuracy relative to the original BFGS method. Among different numerical differentiation techniques, the approximation-based-BFGS method with complex-step achieves outstanding and stable performance in accuracy.
Item Metadata
| Title |
Using complex step numerical differentiation in the Broyden-Fletcher-Goldfard-Shanno algorithm
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| Creator | |
| Supervisor | |
| Publisher |
University of British Columbia
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| Date Issued |
2023
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| Description |
We conduct a study on an alternative method to Derivative-Free Optimization (DFO). It is a method by applying numerical differentiation techniques to the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. We apply different gradient approximation strategies on the BFGS, particularly a complex-step method to the gradient approximation. We conduct an experiment to test the feasibility of the approximation-based-BFGS methods. The experiment also explores the efficiency and reliability of BFGS algorithm with different strategies and different settings. Results find that the approximation-based-BFGS method is feasible alternative to DFO. With appropriate parameter settings, approximation-based-BFGS methods achieve high level accuracy relative to the original BFGS method. Among different numerical differentiation techniques, the approximation-based-BFGS method with complex-step achieves outstanding and stable performance in accuracy.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2023-05-30
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0432738
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2023-09
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| Campus | |
| Scholarly Level |
Graduate
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International