The work deals with the question: how to characterize a given class of real-valued locally Lipschitz functions f(x) in terms of Clarke’s generalized gradient
. Conditions on
necessary and sufficient for f(x) to be (i) quasi-convex and (ii) the difference of convex functions are established. The paper also contains a review of known conditions on
(obtained by R. T. Rockafellar and J. P. Vial) necessary and sufficient for f(x) to belong to the classes of (iii) convex functions, (iv) pointwise supremum of
and(v) semi-smooth functions.