Optimality conditions for lower semi-continuous functions

Let f be a lower semi-continuous and bounded below function from a Banach space X into (-infinity, +infinity] where X is assumed to admit a Lipschitz smooth ''bump-function.'' Generalizing results of Chaney, we study optimality conditions for (x) over bar is an element of X to be a local minimum point of f. These conditions are described in terms of generalized Chaney's subdifferentials and second-order derivatives. (C) 1996 Academic Press, Inc.