Guaranteed Global Deterministic Optimization and Constraint Programming for Complex Dynamic Problems

Abstract

International audienceIn 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