About the Performance of a Calculus-Based Approach to Building Model Functions in a Derivative-Free Trust-Region Algorithm

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...

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Published in:	Algorithms Vol. 16; no. 2; p. 84
Main Authors:	Hare, Warren, Jarry-Bolduc, Gabriel
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01.02.2023
Subjects:	(generalized) simplex gradient Algorithms Analysis Approximation blackbox optimization Calculus calculus-based approach composite objective functions derivative-free algorithms Derivatives Mathematical analysis Mathematical optimization Methods Optimization trust-region methods United Kingdom Germany
ISSN:	1999-4893, 1999-4893
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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.
AbstractList	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.
Audience	Academic
Author	Jarry-Bolduc, Gabriel Hare, Warren
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SubjectTerms	(generalized) simplex gradient Algorithms Analysis Approximation blackbox optimization Calculus calculus-based approach composite objective functions derivative-free algorithms Derivatives Mathematical analysis Mathematical optimization Methods Optimization trust-region methods
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Title	About the Performance of a Calculus-Based Approach to Building Model Functions in a Derivative-Free Trust-Region Algorithm
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