Second-order analysis of the Moreau-Yosida and the Lasry-Lions regularizations
In this paper, we investigate the second-order differentiability properties of the Moreau-Yosida and the Lasry-Lions regularization of a locally Lipschitz continuous function defined on [image omitted]. We give a relationship between the second-order properties of the regularized function and the approximated function itself. These results are useful for convergence analysis of approximate numerical methods for solving non-smooth optimization problems.
moreau-yosida lasry-lions regularization second-order differentiability generalized hessian second-order expansion