Subgradient algorithms on Riemannian manifolds of lower bounded curvatures

Abstract

The subgradient algorithms for convex optimizations on Riemannian Manifolds of sectional curvatures bounded from below are studied; and the convergence results of the algorithms (employing diminishing step sizes and dynamic step sizes) are established. Some numerical experiments are provided to illustrate the convergence performances of the algorithms.

Keywords:

• Riemannian manifold
• convex optimization
• subgradient algorithm
• sectional curvature
• Riemannian center of mass

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

Research of the author was supported in part by the National Natural Science Foundation of China [grant number 11661019]; the Natural Science Foundation of Guizhou Province, China [grant number 20161039].