Weak Sharp Minima and Finite Termination of the Proximal Point Method for Convex Functions on Hadamard Manifolds
arXiv:1205.476320 citationsh-index: 17
Originality Synthesis-oriented
AI Analysis
Provides theoretical convergence guarantees for an optimization method in Riemannian geometry, relevant for non-Euclidean optimization problems.
The paper proves that the proximal point method for convex optimization on Hadamard manifolds terminates in finitely many iterations when the objective function has weak sharp minima on the solution set.
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.