The FermatTorricelli Problem, Part I: A Discrete Gradient-Method Approach
We give a discrete geometric (differential-free) proof of the theorem underlying the solution of the well known FermatTorricelli problem, referring to the unique point having minimal distance sum to a given finite set of non-collinear points in d-dimensional space. Further on, we extend this problem to the case that one of the given points is replaced by an affine flat, and we give also a partial result for the case where all given points are replaced by affine flats (of various dimensions), with illustrative applications of these theorems.
fermattorricelli problem affine flats cauchyschwarz inequality discrete gradient method fasbender duality location science multifocal ellipses steiner minimal trees steinerweber problem varignon frame