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

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...

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Bibliographic Details
Published in:Nonlinear analysis Vol. 64; no. 12; pp. 2787 - 2804
Main Authors: Boţ, Radu Ioan, Wanka, Gert
Format: Journal Article
Language:English
Published: Oxford Elsevier Ltd 15.06.2006
Elsevier
Subjects:
Applied sciences
Calculus of variations and optimal control
Exact sciences and technology
Fenchel duality
Mathematical analysis
Mathematical programming
Mathematics
Operational research and scientific management
Operational research. Management science
Regularity condition
Sciences and techniques of general use
Strong conical hull intersection property
Subdifferential sum formula
Subdifferential sum formula
90C46
90C25
Strong conical hull intersection property
Fenchel duality
49N15
Regularity condition
Subdifferential
Nonlinear analysis
Regularity
90C46 Regularity condition
ISSN:0362-546X, 1873-5215
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-2
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content type line 23
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2005.09.017