Semismoothness of solutions to generalized equations and the Moreau-Yosida regularization

F. Meng, Defeng Sun, G. Zhao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

51 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)561-581
Number of pages21
JournalMathematical Programming
Issue number2-3
Publication statusPublished - 1 Nov 2005
Externally publishedYes


  • Generalized Equations
  • Moreau-Yosida Regularization
  • Semismooth

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

Cite this