On derivative based bounding for simplicial branch and bound

Simplicial based Global Optimization branch and bound methods require tight bounds on the objective function value. Recently, a renewed interest appears on bound calculation based on Interval Arithmetic by Karhbet and Kearfott [ Reliable Comput. 25 (2017) 53–73] and on exploiting second derivative b...

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Published inR.A.I.R.O. Recherche opérationnelle Vol. 55; no. 3; pp. 2023 - 2034
Main Authors Hendrix, Eligius M. T., -Tóth, Boglarka G., Messine, Frederic, Casado, Leocadio G.
Format Journal Article
LanguageEnglish
Published Paris EDP Sciences 01.05.2021
Subjects
Algorithms
Branch and bound methods
Engineering Sciences
Global optimization
Handbooks
Interval arithmetic
Optimization
90C30
Mathematics Subject Classification. 65K05 90C30 90C34
bound / derivative
Mathematics Subject Classification. 65K05
Simplex / branch
90C34
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Summary:Simplicial based Global Optimization branch and bound methods require tight bounds on the objective function value. Recently, a renewed interest appears on bound calculation based on Interval Arithmetic by Karhbet and Kearfott [ Reliable Comput. 25 (2017) 53–73] and on exploiting second derivative bounds by Mohand [ RAIRO Oper. Res. 55 (2021) S2373–S238]. The investigated question here is how partial derivative ranges can be used to provide bounds of the objective function value over the simplex. Moreover, we provide theoretical properties of how this information can be used from a monotonicity perspective to reduce the search space in simplicial branch and bound.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0399-0559
1290-3868
DOI:10.1051/ro/2021081