An optimization problem on the sphere

We prove existence and uniqueness of the minimizer for the average geodesic distance to the points of a geodesically convex set on the sphere. This implies a corresponding existence and uniqueness result for an optimal algorithm for halfspace learning, when data and target functions are drawn from the uniform distribution.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Andreas Maurer
• Keywords: Average Geodesic Distance, Convex Set, CORR 2008, Education, Uniqueness