Weak Sharp Minima and Finite Termination of the Proximal Point Method for Convex Functions on Hadamard Manifolds

TL;DR

This paper proves that the proximal point method terminates finitely for convex functions on Hadamard manifolds if the function has weak sharp minima, extending convergence results to a Riemannian setting.

Contribution

It establishes finite termination of the proximal point method for convex functions with weak sharp minima on Hadamard manifolds, a novel result in Riemannian optimization.

Findings

Finite termination of the proximal point method under weak sharp minima.

Extension of convergence analysis to Hadamard manifolds.

Theoretical proof of finite convergence in Riemannian context.

Abstract

In this paper we proved that the sequence generated by the proximal point method, associated to a unconstrained optimization problem in the Riemannian context, has finite termination when the objective function has a weak sharp minima on the solution set of the problem.