Generalized Hessian matrix and second-order optimality conditions for problems withC 1,1 data

In this paper, we present a generalization of the Hessian matrix toC^1,1 functions, i.e., to functions whose gradient mapping is locally Lipschitz. This type of function arises quite naturally in nonlinear analysis and optimization. First the properties of the generalized Hessian matrix are investigated and then some calculus rules are given. In particular, a second-order Taylor expansion of aC^1,1 function is derived. This allows us to get second-order optimality conditions for nonlinearly constrained mathematical programming problems withC^1,1 data.