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.
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