Second-order subdifferentials of C1,1 functions and optimality conditions

We present second-order subdifferentials of Clarke's type of C^1,1 functions, defined in Banach spaces with separable duals. One of them is an extension of the generalized Hessian matrix of such functions in ⁿ, 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^1,1 data are obtained.This work was partially supported by the National Foundation for Scientific Investigations in Bulgaria under contract No. MM-406/1994.