  In this article, the notion of gH-Clarke derivative for interval-valued
functions is proposed. To define the concept of gH-Clarke derivatives, the
concepts of limit superior, limit inferior, and sublinear interval-valued
functions are studied in the sequel. The upper gH-Clarke derivative of a
gH-Lipschitz interval-valued function (IVF) is observed to be a sublinear IVF.
It is found that every gH-Lipschitz continuous function is upper gH-Clarke
differentiable. For a convex and gH-Lipschitz IVF, it is shown that the upper
gH-Clarke derivative coincides with the gH-directional derivative. The entire
study is supported by suitable illustrative examples.
