A Discussion on Variational Analysis in Derivative-Free Optimization

Variational Analysis studies mathematical objects under small variations. With regards to optimization, these objects are typified by representations of first-order or second-order information (gradients, subgradients, Hessians, etc). On the other hand, Derivative-Free Optimization studies algorithm...

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Bibliographic Details
Published in:Set-valued and variational analysis 2020-12, Vol.28 (4), p.643-659
Main Author: Hare, Warren
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Mathematics
Mathematics and Statistics
Optimization
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Summary:Variational Analysis studies mathematical objects under small variations. With regards to optimization, these objects are typified by representations of first-order or second-order information (gradients, subgradients, Hessians, etc). On the other hand, Derivative-Free Optimization studies algorithms for continuous optimization that do not use first-order information. As such, researchers might conclude that Variational Analysis plays a limited role in Derivative-Free Optimization research. In this paper we argue the contrary by showing that many successful DFO algorithms rely heavily on tools and results from Variational Analysis.
ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-020-00556-y