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

Department of Economics

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

1 Scopus citations

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

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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AU - Lassonde, Marc

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AB - 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.

KW - Convex function

KW - Epi-convergence

KW - Maximal monotone operator

KW - Mosco-convergence

KW - Representative function

KW - Subdifferential

KW - Convex function

KW - Epi-convergence

KW - Maximal monotone operator

KW - Mosco-convergence

KW - Representative function

KW - Subdifferential

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DO - 10.1007/s11590-018-1279-1

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SN - 1862-4472

VL - 13

SP - 795

EP - 803

JO - Optimization Letters

JF - Optimization Letters

IS - 4

ER -

Limits of maximal monotone operators driven by their representative functions

Abstract

Bibliographical note

Keywords

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