Invited Session Wed.3.H 1012

Wednesday, 15:15 - 16:45 h, Room: H 1012

Cluster 17: Nonsmooth optimization [...]

Variational methods in optimization

 

Chair: Nina Ovcharova and Julian Revalski

 

 

Wednesday, 15:15 - 15:40 h, Room: H 1012, Talk 1

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

 

Abstract:
In this work we dropp the condition of convexity and consider both Moreau-Yosida and Lasry-Lions regularizations of locally Lipschitz quadratically minorized functions. Our aim is to investigate the second-order properties of both these regularizations and to relate them to the approximated function itself. For this purpose we consider functions that admit a second-order expanion (e.g., prox-regular functions).
These function possess a generalized Hessian, but note that this
property is weaker than the existence of a classical Hessian, since we
suppose only the existence of the first partial derivatives. We give sufficient conditions for the
regularizations to have a generalized Hessian as well. Emphasize that these results are useful for the convergence analysis of approximate numerical methods for solving nonsmooth optimization problems.

 

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