On derivative based bounding for simplicial branch and bound

Eligius M.T. Hendrix*, Boglarka G. Tóth, Frederic Messine, Leocadio G. Casado

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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.

Original languageEnglish
Pages (from-to)2023-2034
Number of pages12
JournalRAIRO - Operations Research
Issue number3
Early online date1 Jul 2021
Publication statusPublished - 2021


  • Branch and bound
  • Derivative
  • Simplex


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