Boţ, Radu Ioan ; Wanka, Gert : A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces

Author(s):

Boţ, Radu Ioan
Wanka, Gert

Title:

A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 21, 2004

Mathematics Subject Classification:

49N15			[ Duality theory ]
90C25			[ Convex programming ]
90C46			[ Optimality conditions, duality ]

Abstract:

In this paper we present a new regularity condition for the subdifferential sum formula of a convex function with the precomposition of another convex function with a continuous linear mapping. This condition is formulated by using the epigraphs of the conjugates of the functions involved and turns out to be weaker than the generalized interior-point regularity conditions given so far in the literature. Moreover, it provides a weak sufficient condition for Fenchel duality regarding convex optimization problems in infinite dimensional spaces. As an application, we discuss the strong conical hull intersection property (CHIP) for a finite family of closed convex sets.

Keywords:

regularity condition, subdifferential sum formula, Fenchel duality, strong conical hull intersection property

Language:

English

Publication time:

3 / 2005