Equivalence between p-cyclic quasimonotonicity and p-cyclic monotonicity of affine maps

Eladio Ocaña; John Cotrina; Orestes Bueno

doi:10.1080/02331934.2014.891031

Equivalence between p-cyclic quasimonotonicity and p-cyclic monotonicity of affine maps

Eladio Ocaña, John Cotrina, Orestes Bueno

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

Abstract

We prove that the notions of (Formula presented.) -cyclic quasimonotonicity and (Formula presented.) -cyclic monotonicity are equivalent for affine maps defined on Banach spaces. First this is done in a finite dimensional space by using the index of asymmetry for matrices defined by J.-P. Crouzeix and C. Gutan. Then this equivalence is extended to general Banach spaces.

Original language	English
Pages (from-to)	1487-1497
Number of pages	11
Journal	Optimization
Volume	64
Issue number	7
DOIs	https://doi.org/10.1080/02331934.2014.891031
State	Published - 1 Jan 2015

Keywords

affine multivalued maps
cyclic monotonicity
cyclic quasimonotonicity
index of asymmetry
monotonicity+
paramonotonicity
positive semidefinite matrices

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10.1080/02331934.2014.891031

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title = "Equivalence between p-cyclic quasimonotonicity and p-cyclic monotonicity of affine maps",

abstract = "We prove that the notions of (Formula presented.) -cyclic quasimonotonicity and (Formula presented.) -cyclic monotonicity are equivalent for affine maps defined on Banach spaces. First this is done in a finite dimensional space by using the index of asymmetry for matrices defined by J.-P. Crouzeix and C. Gutan. Then this equivalence is extended to general Banach spaces.",

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T1 - Equivalence between p-cyclic quasimonotonicity and p-cyclic monotonicity of affine maps

AU - Ocaña, Eladio

AU - Cotrina, John

AU - Bueno, Orestes

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We prove that the notions of (Formula presented.) -cyclic quasimonotonicity and (Formula presented.) -cyclic monotonicity are equivalent for affine maps defined on Banach spaces. First this is done in a finite dimensional space by using the index of asymmetry for matrices defined by J.-P. Crouzeix and C. Gutan. Then this equivalence is extended to general Banach spaces.

AB - We prove that the notions of (Formula presented.) -cyclic quasimonotonicity and (Formula presented.) -cyclic monotonicity are equivalent for affine maps defined on Banach spaces. First this is done in a finite dimensional space by using the index of asymmetry for matrices defined by J.-P. Crouzeix and C. Gutan. Then this equivalence is extended to general Banach spaces.

KW - affine multivalued maps

KW - cyclic monotonicity

KW - cyclic quasimonotonicity

KW - index of asymmetry

KW - monotonicity+

KW - paramonotonicity

KW - positive semidefinite matrices

KW - affine multivalued maps

KW - cyclic monotonicity

KW - cyclic quasimonotonicity

KW - index of asymmetry

KW - monotonicity+

KW - paramonotonicity

KW - positive semidefinite matrices

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U2 - 10.1080/02331934.2014.891031

DO - 10.1080/02331934.2014.891031

M3 - Article in a journal

SN - 0233-1934

VL - 64

SP - 1487

EP - 1497

JO - Optimization

JF - Optimization

IS - 7

ER -

Equivalence between p-cyclic quasimonotonicity and p-cyclic monotonicity of affine maps

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Keywords

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