Volume 55, Number 3, May-June 2021
|Page(s)||2023 - 2034|
|Published online||01 July 2021|
On derivative based bounding for simplicial branch and bound
Universidad de Málaga, Av Cervantes 2, Málaga, Spain
Wageningen University, Hollandseweg 1, Wageningen, The Netherlands
2 Computational Optimization Dept., University of Szeged, Árpád tér 2, Szeged, Hungary
3 LAPLACE-ENSEEIHT, Toulouse-INP, University of Toulouse, 2 rue Charles Camichel, Toulouse, France
4 Informatics Dept., University of Almería (CeiA3), s/n, 04120 La Cañada, Almería, Spain
* Corresponding author: firstname.lastname@example.org
Accepted: 12 May 2021
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.
Mathematics Subject Classification: 65K05 / 90C30 / 90C34
Key words: Simplex / branch and bound / derivative
© The authors. Published by EDP Sciences, ROADEF, SMAI 2021
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