The Rockafellar Conjecture and type (FPV)

Radu Ioan Boţ; Orestes Bueno; Stephen Simons

doi:10.1007/s11228-016-0384-5

The Rockafellar Conjecture and type (FPV)

Radu Ioan Boţ
, Orestes Bueno
, Stephen Simons

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

1 Scopus citations

Abstract

In this note, using a technique of Verona and Verona, we show that a result announced in “All maximal monotone operators in a Banach space are of type FPV” by A. Eberhard and R. Wenczel, Set-Valued Var. Anal. 22, 597–615, (2014), implies the truth of the Rockafellar conjecture. We then show that there is a gap in the logic of the Eberhard–Wenczel result, which we tried unsuccessfully to close. We also discuss briefly the connection with maximally monotone multifunctions of type (FPV).

Original language	English
Pages (from-to)	381-385
Number of pages	5
Journal	Set-Valued Analysis
Volume	24
Issue number	3
DOIs	https://doi.org/10.1007/s11228-016-0384-5
State	Published - 1 Sep 2016

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SDG 17 Partnerships for the Goals

Keywords

Fenchel conjugate
Maximal monotonicity
Normal cone
Rockafellar’s sum conjecture

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10.1007/s11228-016-0384-5

Cite this

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abstract = "In this note, using a technique of Verona and Verona, we show that a result announced in “All maximal monotone operators in a Banach space are of type FPV” by A. Eberhard and R. Wenczel, Set-Valued Var. Anal. 22, 597–615, (2014), implies the truth of the Rockafellar conjecture. We then show that there is a gap in the logic of the Eberhard–Wenczel result, which we tried unsuccessfully to close. We also discuss briefly the connection with maximally monotone multifunctions of type (FPV).",

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T1 - The Rockafellar Conjecture and type (FPV)

AU - Boţ, Radu Ioan

AU - Bueno, Orestes

AU - Simons, Stephen

PY - 2016/9/1

Y1 - 2016/9/1

N2 - In this note, using a technique of Verona and Verona, we show that a result announced in “All maximal monotone operators in a Banach space are of type FPV” by A. Eberhard and R. Wenczel, Set-Valued Var. Anal. 22, 597–615, (2014), implies the truth of the Rockafellar conjecture. We then show that there is a gap in the logic of the Eberhard–Wenczel result, which we tried unsuccessfully to close. We also discuss briefly the connection with maximally monotone multifunctions of type (FPV).

AB - In this note, using a technique of Verona and Verona, we show that a result announced in “All maximal monotone operators in a Banach space are of type FPV” by A. Eberhard and R. Wenczel, Set-Valued Var. Anal. 22, 597–615, (2014), implies the truth of the Rockafellar conjecture. We then show that there is a gap in the logic of the Eberhard–Wenczel result, which we tried unsuccessfully to close. We also discuss briefly the connection with maximally monotone multifunctions of type (FPV).

KW - Fenchel conjugate

KW - Maximal monotonicity

KW - Normal cone

KW - Rockafellar’s sum conjecture

KW - Fenchel conjugate

KW - Maximal monotonicity

KW - Normal cone

KW - Rockafellar’s sum conjecture

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UR - https://www.scopus.com/pages/publications/84983783144#tab=citedBy

U2 - 10.1007/s11228-016-0384-5

DO - 10.1007/s11228-016-0384-5

M3 - Article in a journal

SN - 0927-6947

VL - 24

SP - 381

EP - 385

JO - Set-Valued Analysis

JF - Set-Valued Analysis

IS - 3

ER -

The Rockafellar Conjecture and type (FPV)

Abstract

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Keywords

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