Write the optimization problem that allows you to find the minimal distance using the Euclidian
norm, between a polyhedron {x ∈ R^n : Ax ≤ b} and a hypersphere of center in $x_{0}$ and radius δ.
It can be formulated as follows:
Minimize: $ d = \| x- x_{0} \|_2 $
Subject to:
$Ax ≤ b$ (some unknown restriction given for the polyhedron i think, the problem doesn't really say anything more)
$\|x - x_{0}\|_{2} >= δ$ (assuming the polyhedron doesn't go inside the hypersphere)
where:
x is a vector of length n representing the coordinates of a point on the polyhedron.
A is a matrix of size m × n representing the constraints on the polyhedron.
b is a vector of length m representing the upper bounds of the constraints.
x₀ is the center of the hypersphere.
δ is the radius of the hypersphere.
$\|.\|_{2}$ denotes the Euclidean norm, which calculates the distance between two points in n-dimensional space. The objective function aims to minimize the Euclidean distance between the point x on the polyhedron and the center x₀ of the hypersphere.
How would you guys solve this problem?
