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

Fac. Math. of the TU

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

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 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.

Original language	English
Pages (from-to)	27-41
Number of pages	15
Journal	Numerical Functional Analysis and Optimization
Volume	28
Issue number	1-2
DOIs	https://doi.org/10.1080/01630560701190224
Publication status	Published - 1 Jan 2007
Externally published	Yes

Keywords

Brézis-Haraux-type approximation
Fitzpatrick function
Maximal monotone operator
Subdifferential

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10.1080/01630560701190224

Cite this

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AU - Bot, Radu Ioan

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

UR - https://www.scopus.com/pages/publications/33947255405

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DO - 10.1080/01630560701190224

M3 - Article

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SP - 27

EP - 41

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 1-2

ER -

Weaker constraint qualifications in maximal monotonicity

Abstract

Keywords

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