Proximal Point Method for Vector Optimization on Hadamard Manifolds

TL;DR

This paper extends the proximal point algorithm for vector optimization from Euclidean spaces to Hadamard manifolds, proving its convergence to weak efficient points under certain conditions.

Contribution

It introduces a novel adaptation of the proximal point method for vector optimization on Hadamard manifolds, expanding its applicability to non-Euclidean geometries.

Findings

Proximal point method is well-defined on Hadamard manifolds.

The method converges to weak efficient points under specific assumptions.

Theoretical convergence guarantees are established.

Abstract

In this paper, we extend the proximal point algorithm for vector optimization from the Euclidean space to the Riemannian context. Under suitable assumptions on the objective function the well definition and full convergence of the method to a weak efficient point is proved.