Abstract
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 language | English |
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Pages (from-to) | 269-281 |
Number of pages | 13 |
Journal | Mathematical Programming, Series B |
Volume | 84 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jan 1999 |
Externally published | Yes |
Keywords
- Moreau
- Piecewise smooth functions
- Yosida regularization
ASJC Scopus subject areas
- Software
- Mathematics(all)