Global Convergence of Hager-Zhang type Riemannian Conjugate Gradient Method

TL;DR

This paper introduces a new Riemannian conjugate gradient method of Hager-Zhang type with exponential retraction, providing global convergence analysis and demonstrating superior numerical performance over existing methods on sphere optimization problems.

Contribution

The paper develops a Hager-Zhang type Riemannian conjugate gradient method with exponential retraction and proves its global convergence under certain assumptions.

Findings

Proposed method outperforms existing methods in numerical experiments.

The method shows higher efficiency in computing the stability number of graphs.

Numerical results confirm the theoretical convergence properties.

Abstract

This paper presents the Hager-Zhang (HZ)-type Riemannian conjugate gradient method that uses the exponential retraction. We also present global convergence analyses of our proposed method under two kinds of assumptions. Moreover, we numerically compare our proposed methods with the existing methods by solving two kinds of Riemannian optimization problems on the unit sphere. The numerical results show that our proposed method has much better performance than the existing methods, i.e., the FR, DY, PRP and HS methods. In particular, they show that it has much higher performance than existing methods including the hybrid ones in computing the stability number of graphs problem.