A derivative free projection method for the singularities of vector fields with convex constraints on Hadamard manifolds

Abstract

The objective of this paper is to introduce a derivative free projection method designed to find the singularities of pseudomonotone vector fields with convex constraints on Hadamard manifolds. This innovative approach combines the hyperplane projection method with a novel search direction. The global convergence of the proposed method is established under certain conditions. Our method improves some existing results in the literature on Hadamard manifolds. Additionally, illustrative numerical examples are provided to demonstrate the practical efficacy of our method. © 2024 Informa UK Limited, trading as Taylor & Francis Group.