Second-order subdifferentials of C functions and optimality conditions.

We present second-order subdifferentials of Clarke's type of C functions, defined in Banach spaces with separable duals. One of them is an extension of the generalized Hessian matrix of such functions in ℝ, considered by J. B. H.-Urruty, J. J. Strodiot and V. H. Nguyen. Various properties of these subdifferentials are proved. Second-order optimality conditions (necessary, sufficient) for constrained minimization problems with C data are obtained. [ABSTRACT FROM AUTHOR]