  This article explores fundamental properties of convex interval-valued
functions defined on Riemannian manifolds. The study employs generalized
Hukuhara directional differentiability to derive KKT-type optimality conditions
for an interval-valued optimization problem on Riemannian manifolds. Based on
type of functions involved in optimization problems, we consider the following
cases:
  1. objective function as well as constraints are real-valued;
  2. objective function is interval-valued, and constraints are real-valued;
  3. objective function as well as constraints are interval-valued.
  The whole theory is justified with the help of examples. The order relation
that we use throughout the paper is a total order relation defined on the
collection of all closed and bounded intervals in $\mathbb{R}$.
