Generalized Hessian Properties of Regularized Nonsmooth Functions

  title={Generalized Hessian Properties of Regularized Nonsmooth Functions},
  author={R. A. Poliquin and R. Tyrrell Rockafellar},
  journal={SIAM Journal on Optimization},
The question of second-order expansions is taken up for a class of functions of importance in optimization, namely Moreau envelope regularizations of nonsmooth functions f . It is shown that when f is prox-regular, which includes convex functions and the extended-real-valued functions representing problems of nonlinear programming, the many second-order properties that can be formulated around the existence and stability of expansions of the envelopes of f or of their gradient mappings are… CONTINUE READING