2011/11/04 by Boris S. Mordukhovich, Mordukhovich, Boris S., Nguyen Mau Nam +4 · 1 citation
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Mathematics and Applications #Optimization and Control (math.OC) #Optimization and Variational Analysis #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1111.1280
openalex publication_date 2011/11/04 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
In this paper we study the following problems: given a finite number of\nnonempty closed subsets of a normed space, find a ball with the smallest radius\nthat encloses all of the sets, and find a ball with the smallest radius that\nintersects all of the sets. These problems can be viewed as generalized\nversions of the smallest enclosing circle problem introduced in the 19th\ncentury by Sylvester which asks for the circle of smallest radius enclosing a\ngiven set of finite points in the plane. We will focus on the sufficient\nconditions for the existence and uniqueness of an optimal solution for each\nproblem, while the study of optimality conditions and numerical implementation\nwill be addressed in our next projects.\n