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Convergence of Subdifferentials of Convexly Composite Functions

Published online by Cambridge University Press:  20 November 2018

C. Combari ,
R. Poliquin  and
L. Thibault
C. Combari
Affiliation:
Université Montpellier II, Laboratoire Analyse Convexe, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France University of Alberta, Department of Mathematical Sciences, Edmonton, Alberta, T6G 2G1
R. Poliquin
Affiliation:
Université Montpellier II, Laboratoire Analyse Convexe, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France University of Alberta, Department of Mathematical Sciences, Edmonton, Alberta, T6G 2G1
L. Thibault
Affiliation:
Université Montpellier II, Laboratoire Analyse Convexe, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France University of Alberta, Department of Mathematical Sciences, Edmonton, Alberta, T6G 2G1
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Abstract

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In this paper we establish conditions that guarantee, in the setting of a general Banach space, the Painlevé-Kuratowski convergence of the graphs of the subdifferentials of convexly composite functions. We also provide applications to the convergence of multipliers of families of constrained optimization problems and to the generalized second-order derivability of convexly composite functions.

Keywords

49A5258C0658C2090C30epi-convergenceMosco convergencePainlevé-Kuratowski convergenceprimal-lower-nice functionsconstraint qualificationslice convergencegraph convergence of subdifferentialsconvexly composite functions
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 2 , 01 April 1999 , pp. 250 - 265
Copyright
Copyright © Canadian Mathematical Society 1999

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