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This article explores fundamental properties of convex interval-valuedfunctions defined on Riemannian manifolds. The study employs generalizedHukuhara directional differentiability to derive KKT-type optimality conditionsfor an interval-valued optimization problem on Riemannian manifolds. Based ontype of functions involved in optimization problems, we consider the followingcases:  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 contraints are interval-valued.  The whole theory is justified with the help of examples. The order relationthat we use throughout the paper is a complete order relation defined on thecollection of all closed and bounded intervals in $\mathbb{R}$.

Optimality Conditions for Interval-Valued Optimization Problems on Riemannian Manifolds Under a Complete Order Relation