Applications of Convex Analysis to the Smallest Intersecting Ball Problem

作者：Nguyen Mau Nam^*; Thai An Nguyen; Salinas Juan

来源：Journal of Convex Analysis, 2012, 19(2): 497-518.

• Convex analysis and optimization
• generalized differentiation
• smallest enclosing ball problem
• smallest intersecting ball problem
• subgradient-type algorithms

The smallest enclosing circle problem asks for the circle of smallest radius enclosing a given set of finite points on the plane. This problem was introduced in the 19th century by Sylvester [17]. After more than a century, the problem remains very active. This paper is the continuation of our effort in shedding new light on classical geometry problems using advanced tools of convex analysis and optimization. We propose and study the following generalized version of the smallest enclosing circle problem: given a finite number of nonempty closed convex sets in a reflexive Banach space, find a ball with the smallest radius that intersects all of the sets.

• 出版日期2012