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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| Published in: | Nonlinear analysis Vol. 64; no. 12; pp. 2787 - 2804 |
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| Main Authors: | , |
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| Language: | English |
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Elsevier Ltd
15.06.2006
Elsevier |
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| ISSN: | 0362-546X, 1873-5215 |
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| 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. |
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| AbstractList | 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. |
| Author | Boţ, Radu Ioan Wanka, Gert |
| Author_xml | – sequence: 1 givenname: Radu Ioan surname: Boţ fullname: Boţ, Radu Ioan email: radu.bot@mathematik.tu-chemnitz.de – sequence: 2 givenname: Gert surname: Wanka fullname: Wanka, Gert email: gert.wanka@mathematik.tu-chemnitz.de |
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| Keywords | Subdifferential sum formula 90C46 90C25 Strong conical hull intersection property Fenchel duality 49N15 Regularity condition Subdifferential Nonlinear analysis Regularity 90C46 Regularity condition |
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| SubjectTerms | 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 |
| Title | A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces |
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