I will give an introduction to the use of methods based on interval arithmetic and their application to global optimization and related problems.
Interval methods allow us to calculate with continuous sets, and hence to rigorously bound the range of a given function over an input region. This in turn allows us to develop algorithms for guaranteed global optimization, root finding and constraint satisfaction.
I will show how these methods can be implemented using the Julia language with the open-source Julia packages that we have been developing for the last few years.
This tutorial presentation was scheduled during the Optimization Days 2020 conference that were cancelled.