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
