Quadratic geometric problems.

[JaromilNajman]

Why this Mod?
There are two quite standard geometric problems which can be solved through quadratic optimization.
The first one is a Minimum Polytope Distance problem, where a user provides 2 sets of n-dimensional points and is interested in the minimal distance between the 2 polytopes defined by the 2 sets.
The second one is a Smallest Enclosing Ball problem, where a user provides a set of n-dimensional points and is interested in the smallest ball enclosing all of the provided points.

Does it fall under an existing category?

• Other: Geometry

What will the API be?

distance, point1, point2 = gurobi_optimods.minpoldist(points1, points2)

where points1,points2 could be a pandas dataframe or alternatively a list.

center,radius = gurobi_optimods.minencball(points)

where points could be a pandas dataframe or alternatively a list.

Additional context
We could add a function which plots the results nicely for 2D problems.
I am not sure how much those problems are used in real world applications. I can image that this could be used in clustering algorithms and statistics but I am not an expert in those fields.