  In this article, the concepts of gH-subgradients and gH-subdifferentials of
interval-valued functions are illustrated. Several important characteristics of
the gH-subdifferential of a convex interval-valued function, e.g., closeness,
boundedness, chain rule, etc. are studied. Alongside, we prove that
gH-subdifferential of a gH-differentiable convex interval-valued function only
contains gH-gradient of that interval-valued function. It is observed that the
gH-directional derivative of a convex interval-valued function in each
direction is maximum of all the products of gH-subgradients and the direction.
Importantly, we show that a convex interval-valued function is gH-Lipschitz
continuous if it has gH-subgradients at each point in its domain. Furthermore,
the relations between efficient solutions of an optimization problem with
interval-valued function and its gH-subgradients are derived.
