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arXiv · 2501.10718

A unified approach to a family of optimization problems in Banach spaces

Kallol Paul·Saikat Roy·Debmalya Sain·Shamim Sohel
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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.

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Kallol Paul, Saikat Roy, Debmalya Sain, Shamim Sohel. 2025-01-18. A unified approach to a family of optimization problems in Banach spaces. https://arxiv.org/abs/2501.10718

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