Properties of the Moreau-Yosida regularization of a piecewise C-2 convex function

Authors
Mifflin, R Qi, LQ Sun, DF
Citation
R. Mifflin et al., Properties of the Moreau-Yosida regularization of a piecewise C-2 convex function, MATH PROGR, 84(2), 1999, pp. 269-281
Citations number
18
Categorie Soggetti
Mathematics
Journal title
MATHEMATICAL PROGRAMMING
ISSN journal
00255610 → ACNP
Volume
84
Issue
2
Year of publication
1999
Pages
269 - 281
Database
ISI
SICI code
0025-5610(199902)84:2<269:POTMRO>2.0.ZU;2-B
Abstract
In this paper we discuss second-order properties of the Moreau-Yosida regul arization F of a piecewise twice continuously differentiable convex functio n f. We introduce a new constraint qualification in order to prove that the gradient of F is piecewise continuously differentiable. In addition, we di scuss conditions, depending on the Hessians of the pieces, that guarantee p ositive definiteness of the generalized Jacobians of the gradient of F.