Constructing a sequence of discrete Hessian matrices of an SC (1) function uniformly convergent to the generalized Hessian matrix
We construct a uniform approximation for generalized Hessian matrix of an SC (1) function. Using the discrete gradient and the extended second order derivative, we define the discrete Hessian matrix. We construct a sequence of sets, where each set is composed of discrete Hessian matrices. We first show some new properties of SC (1) functions. Then, we prove that for SC (1) functions the sequence of the set of discrete Hessian matrices is uniformly convergent to the generalized Hessian matrix.
generalized hessian matrix uniform approximation discrete hessian matrix sc1 functions semismoothness