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About the Performance of a Calculus-Based Approach to Building Model Functions in a Derivative-Free Trust-Region Algorithm Hare, Warren; Jarry-Bolduc, Gabriel

Abstract

This paper examines a calculus-based approach to building model functions in a derivative-free algorithm. This calculus-based approach can be used when the objective function considered is defined via more than one blackbox. Two versions of a derivative-free trust-region method are implemented. The first version builds model functions by using a calculus-based approach, and the second version builds model functions by directly considering the objective function. The numerical experiments demonstrate that the calculus-based approach provides better results in most situations and significantly better results in specific situations.

Item Metadata

Title
About the Performance of a Calculus-Based Approach to Building Model Functions in a Derivative-Free Trust-Region Algorithm
Creator
Hare, Warren; Jarry-Bolduc, Gabriel
Publisher
Multidisciplinary Digital Publishing Institute
Date Issued
2023-02-03
Description
This paper examines a calculus-based approach to building model functions in a derivative-free algorithm. This calculus-based approach can be used when the objective function considered is defined via more than one blackbox. Two versions of a derivative-free trust-region method are implemented. The first version builds model functions by using a calculus-based approach, and the second version builds model functions by directly considering the objective function. The numerical experiments demonstrate that the calculus-based approach provides better results in most situations and significantly better results in specific situations.
Subject
blackbox optimization; derivative-free algorithms; trust-region methods; composite objective functions; calculus-based approach; (generalized) simplex gradient; (generalized) simplex Hessian; quadratic interpolation function
Genre
Article
Type
Text
Language
eng
Date Available
2025-06-12
Provider
Vancouver : University of British Columbia Library
Rights
CC BY 4.0
DOI
10.14288/1.0449108
URI
http://hdl.handle.net/2429/91344
Affiliation
Science, Irving K. Barber Faculty of (Okanagan); Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)
Citation
Algorithms 16 (2): 84 (2023)
Publisher DOI
10.3390/a16020084
Peer Review Status
Reviewed
Scholarly Level
Faculty; Researcher
Rights URI
https://creativecommons.org/licenses/by/4.0/
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CC BY 4.0