Interval methods for scientific computing in Julia
2019-07-25, 11:00–11:30, Elm B

We will show how interval constraint propagation can give a guaranteed description of feasible sets satisfied by nonlinear inequalities via contractors. This technology can be applied to speed up guaranteed global optimization and root finding.

We will give an overview of the suite of inter-related packages making up the JuliaIntervals organization. These are package which use set calculations to solve nonlinear equations, minimize nonlinear functions, and solve ordinary differential equations with results that are (in principle, modulo coding errors!) guaranteed to be correct.

The underlying technique for calculating with sets is interval arithmetic. Here, mathematical operations, such as x -> x^2 and x + y are defined on sets, represented as intervals of all real numbers between two endpoints. By defining these operations carefully, we can guarantee that f(X) is guaranteed to contain f(x) for all x in the set X, even though we use floating-point arithmetic for the calculations.

A key technique is interval contraint propagation, which allows us to calculate enclosures of the inverse of a given function. We will show how this can accelerate optimisation and root finding using interval methods.

The presentation will be based on practical applications.

Co-authors – Luis Benet