Facility location in normed linear spaces

Abstract

We study the Fermat-Torricelli problem in the framework of normed linear spaces by using some ingredients of convex analysis and optimization. Several general formulations of the Fermat-Torricelli problem are presented. Sufficient conditions for the existence and uniqueness of the minimum point are formulated. Existence conditions for the minimum point are related to reflexivity assumptions on the normed space. Uniqueness conditions are related to strict convexity assumptions on the normed space. In the second part of the paper we study the Fermat problem subject to constraints in the plane and on the sphere.

On Fermat-Torricelli Problem in Frechet Spaces

“…In particular, we consider the existence of Torricellian points in Frechet spaces and as a proposition, we state the properties of functional which recaptures similar results in Dragomir and Comanescu ([3], proposition 1). This work complements the results of authors in [3,4,14] and also extends Ayinde and Osinuga [1]. The main aim of this paper is to investigate and generalize Proposition (2.3) of [13], Propositions (4.2, 4.3 and 5.1) of [4] for the case when X is a Frechet space.…”

“…The following authors worked on the FTP in normed linear spaces (nls), reflexive nls, reflexive Banach spaces, inner product spaces (i.p.s) and normed planes and spaces respectively: Radulescu et al [14], Vesely [21], Papini and Puerto [13], Dragomir and Comanescu [3], Dragomir et al [4] and Matrini et al [9]. In recent time, Radulescu et al [14] obtained several general formulations of FTP in nls by using theory of convex analysis and optimization. Vesely [21] established results on the FTP in nls that are reflexive.…”