Second-order analysis of the Moreau–Yosida and the Lasry–Lions regularizations

Abstract

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 . 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.

Keywords:

• generalized Hessian
• second-order expansion
• Moreau–Yosida
• Lasry–Lions regularization
• second-order differentiability

AMS Subject Classification :

• 49J52
• 58C20