# An optimization problem on the sphere

@article{Maurer2008AnOP, title={An optimization problem on the sphere}, author={Andreas Maurer}, journal={ArXiv}, year={2008}, volume={abs/0805.2362} }

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.

#### Topics from this paper

#### One Citation

A Uniform Lower Error Bound for Half-Space Learning

- Mathematics, Computer Science
- ALT
- 2008

It is argued that the lower bound for the error of any unitarily invariant algorithm learning half-spaces against the uniform or related distributions on the unit sphere is well suited to evaluate the benefits of multi-task or transfer learning, or other cases where an expense in the acquisition of domain knowledge has to be justified. Expand

#### References

SHOWING 1-3 OF 3 REFERENCES

A concept of the mass center of a system of material points in the constant curvature spaces

- Mathematics
- 1993

This article demonstrates that in the Lobatchevsky space and on a sphere of arbitrary dimensions, the concept of the mass center of a system of mass points can be correctly defined. Presented are: a… Expand

Spherical averages and applications to spherical splines and interpolation

- Mathematics, Computer Science
- TOGS
- 2001

A method for computing weighted averages on spheres based on least squares minimization that respects spherical distance is introduced, and existence and uniqueness properties of the weighted averages are proved, and fast iterative algorithms with linear and quadratic convergence rates are given. Expand