HAL CCSD
Resolution of nonlinear interval problems using symbolic interval arithmetic
Jaulin, Luc
Chabert, Gilles
Développement des Technologies Nouvelles (DTN) ; École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)
WOS
International audience
ISSN: 0952-1976
Engineering Applications of Artificial Intelligence
Elsevier
hal-00531534
https://ensta-bretagne.hal.science/hal-00531534
https://ensta-bretagne.hal.science/hal-00531534
Engineering Applications of Artificial Intelligence, 2010, 23 (6), pp.1035-1049. ⟨10.1016/j.engappai.2009.06.002⟩
DOI: 10.1016/j.engappai.2009.06.002
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.engappai.2009.06.002
en
Interval analysis
Quantified problems
Symbolic intervals
Constraint propagation
Nonlinear problems
info:eu-repo/semantics/article
Journal articles
An interval problem is a problem where the unknown variables take interval values. Such a problem can be defined by interval constraints, such as “the interval [a,b]subset of[a,b]2”. Interval problems often appear when we want to analyze the behavior of an interval solver. To solve interval problems, we propose to transform the constraints on intervals into constraints on their bounds. For instance, the previous interval constraint [a,b]subset of[a,b]2 can be transformed into the following bound constraints “a≥min(a2,ab,b2) and b≤max(a2,ab,b2)”. Classical interval solvers can then be used to solve the resulting bound constraints. The procedure which transforms interval constraints into equivalent bound constraints can be facilitated by using symbolic interval arithmetic. While classical intervals can be defined as a pair of two real numbers, symbolic intervals can be defined as a pair of two symbolic expressions. An arithmetic similar to classical interval arithmetic can be defined for symbolic intervals. The approach will be illustrated on several applications.
2010