Proximal Point Method for a Special Class of Nonconvex Functions on Hadamard Manifolds

TL;DR

This paper introduces a proximal point method tailored for a specific class of nonconvex functions on Hadamard manifolds, ensuring sequence well-definedness, convergence, and optimality conditions.

Contribution

It extends proximal point algorithms to nonconvex functions on Hadamard manifolds with convergence guarantees and optimality analysis.

Findings

Sequence generated by the method is well-defined.

Accumulation points satisfy necessary optimality conditions.

Convergence to a minimizer is established under additional assumptions.

Abstract

In this paper we present the proximal point method for a special class of nonconvex function on a Hadamard manifold. The well definedness of the sequence generated by the proximal point method is guaranteed. Moreover, it is proved that each accumulation point of this sequence satisfies the necessary optimality conditions and, under additional assumptions, its convergence for a minimizer is obtained.