Limits of maximal monotone operators driven by their representative functions

Yboon García; Marc Lassonde

doi:10.1007/s11590-018-1279-1

Limits of maximal monotone operators driven by their representative functions

Yboon García, Marc Lassonde

Research output: Contribution to journal › Article in a journal › peer-review

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Abstract

In a previous paper, the authors showed that in a reflexive Banach space the lower limit of a sequence of maximal monotone operators is always representable by a convex function. The present paper gives precisions to the latter result by demonstrating the continuity of the representation with respect to the epi-convergence of the representative functions, and the stability of the class of maximal monotone operators with respect to the Mosco-convergence of their representative functions.

Original language	English
Pages (from-to)	795-803
Number of pages	9
Journal	Optimization Letters
Volume	13
Issue number	4
DOIs	https://doi.org/10.1007/s11590-018-1279-1
State	Published - 1 Jun 2019

Bibliographical note

Publisher Copyright: © 2018, Springer-Verlag GmbH Germany, part of Springer Nature. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

Convex function
Epi-convergence
Maximal monotone operator
Mosco-convergence
Representative function
Subdifferential

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10.1007/s11590-018-1279-1

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KW - Mosco-convergence

KW - Representative function

KW - Subdifferential

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JO - Optimization Letters

JF - Optimization Letters

IS - 4

ER -

Limits of maximal monotone operators driven by their representative functions

Abstract

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Keywords

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