A unified approach to a family of optimization problems in Banach spaces
Abstract
Our principal aim is to illustrate that the concept Birkhoff-James orthogonality can be applied effectively to obtain a unified approach to a large family of optimization problems in Banach spaces. We study such optimization problems from the perspective of Birkhoff-James orthogonality in certain suitable Banach spaces. In particular, we demonstrate the duality between the Fermat-Torricelli problem and the Chebyshev center problem which are important particular cases of the least square problem. We revisit the Fermat-Torricelli problem for three and four points and solve it using the same technique. We also investigate the behavior of the Fermat-Torricelli points under the addition or replacement of a new point, and present several new results involving the locations of the Fermat-Torricelli point and the Chebyshev center.
Keywords
Cite
@article{arxiv.2501.10718,
title = {A unified approach to a family of optimization problems in Banach spaces},
author = {Kallol Paul and Saikat Roy and Debmalya Sain and Shamim Sohel},
journal= {arXiv preprint arXiv:2501.10718},
year = {2025}
}