Shortest distance to a point

[schillic]

Given a set X and a point p (and maybe a distance function d), compute the minimal distance of X and p:

min_{x ∈ X} d(x, p)

For some distances (e.g., Euclidean) this is doable (see for instance polytope-closest-point).

[ueliwechsler]

This could also be done by using an implementation of the GJK algorithm #920. However, I think this would not be the most efficient way to compute the shortest distance.

[mforets]

There are some implementations using LazySets types and JuMP to perform the optimization in the package https://github.com/sisl/NeuralPriorityOptimizer.jl/blob/main/src/utils.jl