2ND-ORDER SUBGRADIENTS OF CONVEX INTEGRAL FUNCTIONALS

Authors
MOUSSAOUI M SEEGER A
Citation
M. Moussaoui et A. Seeger, 2ND-ORDER SUBGRADIENTS OF CONVEX INTEGRAL FUNCTIONALS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 318(7), 1994, pp. 613-618
Citations number
10
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
318
Issue
7
Year of publication
1994
Pages
613 - 618
Database
ISI
SICI code
0764-4442(1994)318:7<613:2SOCIF>2.0.ZU;2-N
Abstract
In this Note we give several equivalent characterizations of the set p artial-derivative2 F (xBAR, yBAR), known as the second-order subdiffer ential of F at xBAR relative to yBAR is-an-element-of partial-derivati ve F (xBAR). Here F is a convex function defined over a reflexive Bana ch space. Then we establish a formula for computing the second-order s ubdifferential partial-derivative2 I(f) (xBAR, yBAR) of a convex integ ral functional I(f) defined over an L(p)-space.