Bot, Radu Ioan ; Grad, Sorin Mihai ; Wanka, Gert : A new constraint qualification for the formula of the subdifferential of composed convex functions in infinite dimensional spaces

Author(s):

Bot, Radu Ioan
Grad, Sorin Mihai
Wanka, Gert

Title:

A new constraint qualification for the formula of the subdifferential of composed convex functions in infinite dimensional spaces

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 11, 2005

Mathematics Subject Classification:

90C25			[ Convex programming ]
42A50			[ Conjugate functions, conjugate series, singular integrals ]
49N15			[ Duality theory ]

Abstract:

We give equivalent statements for the formulae of the conjugate function of the sum between a convex lower-semicontinuous function and the precomposition of another convex lower-semicontinuous function which is also K - increasing with a K - convex lower-semicontinuous function, where K is a non-empty closed convex cone and we work in locally convex spaces. These statements prove to be new and weak constraint qualifications under which the formulae for the subdifferential of the mentioned sum of functions are valid. Then we deliver some constraint qualifications inspired from them that guarantee some conjugate duality assertions. Two interesting special cases taken from the literature conclude the paper.

Keywords:

conjugate functions, constraint qualifications, epigraphs, subdifferentials

Language:

English

Publication time:

8 / 2005