A technical note on "The KKT Optimality Conditions For Optimization Problem With Interval-Valued Objective Function On Hadamard Manifolds"

Abstract

In this technical note, we disprove S.-L. Chen's \cite{chen} assertion that the generalized Hukuhara directional differentiability of an interval-valued function defined on a Hadamard manifold is fully identical to the directional differentiability of its endpoint functions by providing a counterexample. Moreover, we address imprecisions in several results proved by using the aforementioned assertion in \cite{chen}. We provide correct statements of the imprecise results and construct examples in their support