Convergence and rate of convergence of a non-autonomous gradient system on Hadamard manifolds.

In this paper we consider the following nonhomogeneous gradient system on a Hadamard manifold M where φ: M → ℝ is a geodesically convex function of class C with argmin φ ≠ Ø. We prove global convergence of solutions of the gradient systemto a minimum point of φ. We also discuss on the rate of convergence of φ( x( t)) to the minimum value of φ as well as the rate of convergence of | x′( t)| and d( x( t), p) to zero, where p is the minimum point of φ. Finally, we present some problems and future directions to study. [ABSTRACT FROM AUTHOR]