Some formulae of convex and nonconvex duality
type: Item
instance of: scholarly article
title: Some formulae of convex and nonconvex duality
zbMATH Open document ID: 0810.49038
DOI: 10.1007/BF01027112
author: M. Volle
published in: Set-Valued Analysis
publication date: 1995-04-06T00:00:00Z
review text: Dans la première partie du travail on est mis en lumière, que la condition de qualification de type géométrique donnée par \textit{H. Attouch} et \textit{H. Brézis} [Aspects of mathematics and its applications, Collect. Pap. Hon. L. Nachbin, 125-133 (1986; Zbl 0642.46004)] permet de donner des résultats sur la sous- différentiabilité de l'inf-convolution de deux fonctions sur un espace de Banach. Successivement on fait application de cette condition à l'optimisation et à la dualité dans le cadre non convexe, de sorte que vient retrouvé la formule de \textit{J.-B. Hiriart-Urruty} [Can. Math. Bull. 29, 482-485 (1986; Zbl 0608.90087)] sur la conjuguée d'une différence de fonctions convexes.
Mathematics Subject Classification ID: 49N15
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 627482
zbMATH Keywords: convex duality
zbMATH Keywords: nonconvex duality
zbMATH Keywords: subdifferentiability
zbMATH Keywords: inf-convolution
reviewed by: Silvio Cinquini
MaRDI profile type: Publication
cites work: Q3784617
cites work: Q3782303
cites work: Convex Functions with Unbounded Level Sets and Applications to Duality Theory
cites work: Partially finite convex programming. I: Quasi relative interiors and duality theory
cites work: Convex analysis and measurable multifunctions
cites work: Q4767831
cites work: Q3679786
cites work: A Comparison of Constraint Qualifications in Infinite-Dimensional Convex Programming
cites work: A General Formula on the Conjugate of the Difference of Functions
cites work: Duality and infinite dimensional optimization
cites work: Well-posedness, condition number, and good asymptotic behaviour
cites work: Convex Analysis
cites work: Q4050397
cites work: Conjugate functions and subdifferentials in nonnormed situations for operators with complete graphs
cites work: The occasional distributivity of ∘ over+e and the change of variable formula for conjugate functions
cites work: A Fenchel-Rockafellar type duality theorem for maximization
cites work: Duality in nonconvex optimization
cites work: Solvability results for sublinear functions and operators
cites work: On uniformly convex functions
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description: scientific article; zbMATH DE number 627482