For a project, I need to research a math and computer science problem. However, I am not sure what is the name of this problem.
I have N dimensions, each dimension has an upper and a lower bound. In this space, I possess p points. Now I want to find a new location of a point that is the farther apart from all the other points but still is inside the space.
I looked Voronoi diagram, p-dispersion problem, the metric k-center, but none of them seems to fit my problem setting.
If you know the name of this problem and/or the name of the algorithm that can solve it, it would be very much appreciated!
It looks like you are on the concept of "farthest-point" Voronoi diagram which in a certain sense is dual to the closest point Voronoi diagram. See the last 10 slides of this excellent presentation.
Here is (see figure) an example issued from the Ph.D. thesis of Michel GOEB (references at the bottom of this answer) involving this concept in the framework of the measure of the set of circles including a certain set of points and excluding another set of points (This figure is extracted from his thesis).
These concepts can be extended from 2D to nD.
Fig. 1: Voronoi cells associated to 5 points: the "ordinary Voronoi" ones in red and the "Farthest Voronoi" in blue, with on the right, a 3D lifting of the left figure, one of the results of this Ph.D. thesis making a connection with a polyhedron obtained from tangent planes to paraboloid $z=x^2+y^2$.
References: Michel GOEB, "Modèles géométriques et mesures d'ensembles de cercles contraints", defended on the 2 Dec. 2008, Université de Saint-Etienne, France (I was the director of this Ph.D. thesis)