Using complex step numerical differentiation in the Broyden-Fletcher-Goldfard-Shanno algorithm
department or school: Science, Irving K. Barber Faculty of (Okanagan)
department or school: Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)
data provider: DSpace
degree campus: UBCO
creator: Chen, Jinghong
issued: 2023-05-30T08:04:51Z
issued: 2023
related degree: Master of Science - MSc
degree grantor: University of British Columbia
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.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/84716
note: Using Complex Step NumericalDifferentiation in theBroyden-Fletcher-Goldfard-ShannoAlgorithmbyJinghong ChenA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE COLLEGE OF GRADUATE STUDIES(Computer Science)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)May 2023© Jinghong Chen, 2023The following individuals certify that they have read, and recommendto the College of Graduate Studies for acceptance, a thesis/dissertation en-titled:Using Complex Step Numerical Differentiation in the Broy-den-Fletcher-Goldfard-Shanno Algorithmsubmitted by Jinghong Chen in partial fulfilment of the requirements ofthe degree of Master of ScienceWarren Hare, I. K. Barber Faculty of ScienceSupervisorPeter J. Simpson, I. K. Barber Faculty of ScienceSupervisory Committee MemberMohamed Shehata, I. K. Barber Faculty of ScienceSupervisory Committee MemberYang Cao, School of EngineeringUniversity ExamineriiAbstractWe conduct a study on an alternative method to Derivative-Free Opti-mization (DFO). It is a method by applying numerical differentiation tech-niques to the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. Weapply different gradient approximation strategies on the BFGS, particularlya complex-step method to the gradient approximation. We conduct an ex-periment to test the feasibility of the approximation-based-BFGS methods.The experiment also explores the efficiency and reliability of BFGS algo-rithm with different strategies and different settings.Results find that the approximation-based-BFGS method is feasible al-ternative to DFO. With appropriate parameter settings, approximation-based-BFGS methods achieve high level accuracy relative to the originalBFGS method. Among different numerical differentiation techniques, theapproximation-based-BFGS method with complex-step achieves outstand-ing and stable performance in accuracy.iiiLay SummaryThe Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is an out-standing method for optimization problems…
has type: Thesis/Dissertation
date issued: 2023-09
is shown at: 10.14288/1.0432738
language: eng
degree discipline: Computer Science
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
contributor: Hare, Warren
type: Text
identifier URI: http://hdl.handle.net/2429/84716