Abstract
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.
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This paper is dedicated to Terry Rockafellar on the occasion of his seventieth birthday
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Meng, F., Sun, D. & Zhao, G. Semismoothness of solutions to generalized equations and the Moreau-Yosida regularization. Math. Program. 104, 561–581 (2005). https://doi.org/10.1007/s10107-005-0629-9
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DOI: https://doi.org/10.1007/s10107-005-0629-9