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

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Resumen

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).

Idioma original	Inglés
Páginas (desde-hasta)	381-385
Número de páginas	5
Publicación	Set-Valued and Variational Analysis
Volumen	24
N.º	3
DOI	https://doi.org/10.1007/s11228-016-0384-5
Estado	Publicada - 1 set. 2016

Palabras clave

Fenchel conjugate
Maximal monotonicity
Normal cone
Rockafellar’s sum conjecture

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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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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 and Variational Analysis

JF - Set-Valued and Variational Analysis

IS - 3

ER -

The Rockafellar Conjecture and type (FPV)

Resumen

Palabras clave

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