Weaker constraint qualifications in maximal monotonicity

Radu Ioan Bot; Sorin Mihai Grad; Gert Wanka

doi:10.1080/01630560701190224

Weaker constraint qualifications in maximal monotonicity

Radu Ioan Bot
, Sorin Mihai Grad
, Gert Wanka

Faculty of Mathematics
Fac. Math. of the TU

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

13 Citations (Scopus)

Résumé

We give a sufficient condition, weaker than the others known so far, that guarantees that the sum of two maximal monotone operators on a reflexive Banach space is maximal monotone. Then we give a weak constraint qualification assuring the Brézis-Haraux-type approximation of the range of the sum of the subdifferentials of two proper convex lower-semicontinuous functions in nonreflexive Banach spaces, extending and correcting an earlier result due to Riahi.

langue originale	Anglais
Pages (de - à)	27-41
Nombre de pages	15
journal	Numerical Functional Analysis and Optimization
Volume	28
Numéro de publication	1-2
Les DOIs	https://doi.org/10.1080/01630560701190224
état	Publié - 1 janv. 2007
Modification externe	Oui

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10.1080/01630560701190224

Contient cette citation

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abstract = "We give a sufficient condition, weaker than the others known so far, that guarantees that the sum of two maximal monotone operators on a reflexive Banach space is maximal monotone. Then we give a weak constraint qualification assuring the Br{\'e}zis-Haraux-type approximation of the range of the sum of the subdifferentials of two proper convex lower-semicontinuous functions in nonreflexive Banach spaces, extending and correcting an earlier result due to Riahi.",

keywords = "Br{\'e}zis-Haraux-type approximation, Fitzpatrick function, Maximal monotone operator, Subdifferential",

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AU - Grad, Sorin Mihai

AU - Wanka, Gert

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N2 - We give a sufficient condition, weaker than the others known so far, that guarantees that the sum of two maximal monotone operators on a reflexive Banach space is maximal monotone. Then we give a weak constraint qualification assuring the Brézis-Haraux-type approximation of the range of the sum of the subdifferentials of two proper convex lower-semicontinuous functions in nonreflexive Banach spaces, extending and correcting an earlier result due to Riahi.

AB - We give a sufficient condition, weaker than the others known so far, that guarantees that the sum of two maximal monotone operators on a reflexive Banach space is maximal monotone. Then we give a weak constraint qualification assuring the Brézis-Haraux-type approximation of the range of the sum of the subdifferentials of two proper convex lower-semicontinuous functions in nonreflexive Banach spaces, extending and correcting an earlier result due to Riahi.

KW - Brézis-Haraux-type approximation

KW - Fitzpatrick function

KW - Maximal monotone operator

KW - Subdifferential

U2 - 10.1080/01630560701190224

DO - 10.1080/01630560701190224

M3 - Article

AN - SCOPUS:33947255405

SN - 0163-0563

VL - 28

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EP - 41

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 1-2

ER -

Weaker constraint qualifications in maximal monotonicity

Résumé

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