Guaranteed Global Deterministic Optimization and Constraint Programming for Complex Dynamic Problems

Hugo Joudrier (1) , Khaled Hadj-Hamou (1)

1 G-SCOP_ROSP - Recherche Opérationnelle pour les Systèmes de Production

In this article we focus on particular multi-physics (mechanic, magnetic, electronic...) dynamic problems. These problems contain some differential constraints to model dynamic behaviors. The goal is to be able to solve it with guarantee, meaning to get a proof that all constraints are satisfied (without any approximation caused by binary representations or rounding modes from the unit core computing). The idea of getting guarantees on the arithmetic operations has been introduced via Interval Arithmetic. Computers become faster gradually, increasing the rate of operations number computable in one time unit. The results computed are often rounded to the nearest representable values, then the global errors are increasing gradually as well without any control over it.

Mots clés: Global Optimization; Ordinary Differential Equation; Interval Arithmetic; Tube Arithmetic; Constraint Programming

Domaines: Analyse numérique [cs.NA]; Recherche opérationnelle [math.OC]; Systèmes dynamiques [math.DS]

Hugo Joudrier, Khaled Hadj-Hamou. Guaranteed Global Deterministic Optimization and Constraint Programming for Complex Dynamic Problems. 21th International Conference on Principles and Practice of Constraint Programming, Aug 2015, Cork, Ireland. ⟨hal-01244426v2⟩