We show that a locally Lipschitz homeomorphism function is semismooth at a given point if and only if its inverse function is semismooth at its image point. We present a sufficient condition for the semismoothness of solutions to generalized equations over cone reducible (nonpolyhedral) convex sets. We prove that the semismoothness of solutions to the Moreau-Yosida regularization of a lower semicontinuous proper convex function is implied by the semismoothness of the metric projector over the epigraph of the convex function. © Springer-Verlag 2005.
|Number of pages||21|
|Publication status||Published - 1 Nov 2005|
- Generalized Equations
- Moreau-Yosida Regularization
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