Facility Location Problem in Pre-Inner Product Spaces
Abstract
In this paper, we define the Fermat-Torricelli problem for the set of n fixed points in metrizable locally convex spaces with the aid of countable collection of continuous seminorms as gauges. The concept of Fermat-Torricelli problem for pre-inner product space H is formulated, with H being the projective limit of sequence of inner product spaces. Similarly, the existence and uniqueness of a minimizer of FermatTorricelli problem in pre-inner product spaces are shown