A generalized geometric spectral conjugate gradient algorithm for finding zero of a monotone tangent vector field on a constant curvature Hadamard manifold

Abstract

This paper is concerned with the problem of finding a zero of a monotone tangent vector field on a constant curvature Hadamard manifold. We propose a geometric spectral conjugate gradient method for solving this problem. The global convergence of the proposed method is established under some conditions. Illustrative numerical examples are also presented to show the practical effectiveness of our method.