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

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
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