Characterizations of weak sharp minima for lower-C1 functions

We derive characterizations of weak sharp minimizers of order one for the class of lower-C1 functions. The characterizations of such minimizers are obtained for a nonlinear programming problem with an abstract set constraint. The first characterization is formulated in terms of the proximal normals to a given set relative to the abstract set constraint, and the directional derivative of the objective function. Two examples are given to illustrate this characterization. The other characterizations are extensions of the main characterizations of weak sharp minima for convex functions, recently proved by Burke and Deng (2002) [13, Theorems 2.2 and 2.3], to the class of lower-C1 functions.