Work

A Generalized Sylvester Problem and a Generalized Fermat-Torricelli Problem

Year: 2013

Type: article

Abstract: We introduce and study the following problem and its further generalizations: given two finite collections of sets in a normed space, find a ball whose center lies in a given constraint set with the smallest radius that encloses all the sets in the first collection and intersects all the sets in the second one. This problem can be considered as a generalized version of the Sylvester smallest enclosing circle problem introduced in the 19th century by Sylvester which asks for the circle of smallest radius enclosing a given set of finite points in the plane. We also consider a generalized version of the Fermat-Torricelli problem: given two finite collections of sets in a normed space, find a point in a given constraint set that minimizes the sum of the farthest distances to the sets in the first collection and shortest distances (distances) to the sets in the second collection.

Source: Journal of convex analysis

DOI: 10.68381/jca20038

Authors: Nguyen Mau Nam, Hoang Nguyen

Institutions: Portland State University, Hue University, Hue University of Education

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funder: National Foundation for Science and Technology Development

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