On derivative based bounding for simplicial branch and bound

¹ 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: eligius@uma.es

Received: 22 December 2020
Accepted: 12 May 2021

Abstract

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.