Year: 2024
Type: article
Abstract: In deterministic global optimization, techniques for linear relaxation of a non-convex program are used in the lower bound calculation phase. To achieve this phase, most deterministic global optimization codes use reformulation-linearization techniques. However, there exist also two interval-based polyhedral relaxation techniques which produce reliable bounds without adding new auxiliary variables, and which can take into account mathematical operations and most transcendental functions: (i) the affine relaxation technique, used in the IBBA code, based on affine forms and affine arithmetic, and (ii) the extremal Taylor technique, used in the Ibex-Opt code, which is based on a specific interval-based Taylor form. In this paper, we describe how these two interval-based linear relaxation techniques can be hybridized. These two approaches appear to be complementary, and such a hybrid method performs well on a representative sample of constrained global optimization instances.
Source: Journal of Global Optimization
Institutions: Pontificia Universidad Católica de Valparaíso, Centre National de la Recherche Scientifique, Laboratoire Plasma et Conversion d'Energie, Université de Toulouse, Laboratoire des Sciences et Techniques de l’Information de la Communication et de la Connaissance, École nationale supérieure de techniques avancées Bretagne, Université de Montpellier
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,890
OpenAlex ID: W4404731437