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RESEARCH PRODUCT

Optimal Locations and Inner Products

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Abstract In a normed space X , we consider objective functions which depend on the distances between a variable point and the points of certain finite sets A . A point where such a function attains its minimum on X is generically called an optimal location. In this paper we obtain characterizations of inner product spaces with properties connecting optimal locations and the convex hull of A or barycenters of points of A with well chosen weights. We thus generalize several classical results about characterization of inner product spaces.