Long Time Behavior of Quasi-convex and Pseudo-convex Gradient Systems on Riemannian Manifolds

Abstract

The paper studies a gradient system of quasi-convex type in
Riemannian manifolds. We prove convergence of the gradient system of a
quasi-convex and pseudo-convex function to a critical point or a minimum
point of them on Riemannian and Hadamard manifolds. We also study the
discrete case of the system in inexact case that it can be useful in
optimization.