As part of a recent research problem, I needed a cheap and sharp way to compute anytime-valid refineable lower bounds for directional derivatives of a high-dimensional function over a coordinate diamond. The Interval Branch and Bound (B&B) algorithm turned out to be a good fit for this task. In this talk I will tell you about the Mathematics involved in this algorithm – including the so-called “Fundamental Theorem of Interval Arithmetic” – as well as its history and the context I had to apply it in.
A Conservative Optimization Algorithm Using the Fundamental Theorem of Interval Arithmetic
A Conservative Optimization Algorithm Using the Fundamental Theorem of Interval Arithmetic