Institute of Mathematics with Computer Center at the Bulgarian Academy of Sciences
We present second-order subdifferentials of Clarke’s type of C^1,1 functions, defined in separable Banach spaces with separable duals, i.e. of functions whose gradient mapping is locally Lipschitz. One of them is an extension of the generalized Hessian matrix of such functions in R^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.