Properties of the Moreau-Yosida regularization of a piecewise C2convex function

Defeng Sun, Robert Mifflin, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

17 Citations (Scopus)


In this paper we discuss second-order properties of the Moreau-Yosida regularization F of a piece-wise twice continuously differentiable convex function f. We introduce a new constraint qualification in order to prove that the gradient of F is piecewise continuously differentiable. In addition, we discuss conditions, depending on the Hessians of the pieces, that guarantee positive definiteness of the generalized Jacobians of the gradient of F.
Original languageEnglish
Pages (from-to)269-281
Number of pages13
JournalMathematical Programming, Series B
Issue number2
Publication statusPublished - 1 Jan 1999
Externally publishedYes


  • Moreau
  • Piecewise smooth functions
  • Yosida regularization

ASJC Scopus subject areas

  • Software
  • General Mathematics


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