Conditioning for optimization problems under general perturbations

Monica Bianchi; G. Kassay; R. Pini; Rita Pini

doi:10.1016/j.na.2011.07.061

Conditioning for optimization problems under general perturbations

Monica Bianchi, G. Kassay, R. Pini, Rita Pini

Risultato della ricerca: Contributo in rivista › Articolo in rivista › peer review

5 Citazioni (Scopus)

Abstract

Given a function f in the class C^(1,1)B(0, r), where B(0, r) denotes a ball of radius r in a real Banach space E, we provide the definition of a positive extended real number c*(f ) defined through the function, that plays a role in the study of the sensitivity of the Argmin map of the perturbed function F_g (p, u) = f (u) − g(p, u). This number coincides with the number c_2(f ) introduced by Zolezzi (2003) if linear perturbations g(p, u) = <p, u> are considered.

Lingua originale	English
pagine (da-a)	37-45
Numero di pagine	9
Rivista	NONLINEAR ANALYSIS
Volume	2012
DOI	https://doi.org/10.1016/j.na.2011.07.061
Stato di pubblicazione	Pubblicato - 2012

Keywords

condition number theory
convex optimization
sensitivity

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10.1016/j.na.2011.07.061

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title = "Conditioning for optimization problems under general perturbations",

abstract = "Given a function f in the class C^(1,1)B(0, r), where B(0, r) denotes a ball of radius r in a real Banach space E, we provide the definition of a positive extended real number c*(f ) defined through the function, that plays a role in the study of the sensitivity of the Argmin map of the perturbed function F_g (p, u) = f (u) − g(p, u). This number coincides with the number c_2(f ) introduced by Zolezzi (2003) if linear perturbations g(p, u) = are considered.",

keywords = "condition number theory, convex optimization, sensitivity, condition number theory, convex optimization, sensitivity",

author = "Monica Bianchi and G. Kassay and R. Pini and Rita Pini",

year = "2012",

doi = "10.1016/j.na.2011.07.061",

language = "English",

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journal = "NONLINEAR ANALYSIS",

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T1 - Conditioning for optimization problems under general perturbations

AU - Bianchi, Monica

AU - Kassay, G.

AU - Pini, R.

AU - Pini, Rita

PY - 2012

Y1 - 2012

N2 - Given a function f in the class C^(1,1)B(0, r), where B(0, r) denotes a ball of radius r in a real Banach space E, we provide the definition of a positive extended real number c*(f ) defined through the function, that plays a role in the study of the sensitivity of the Argmin map of the perturbed function F_g (p, u) = f (u) − g(p, u). This number coincides with the number c_2(f ) introduced by Zolezzi (2003) if linear perturbations g(p, u) = are considered.

AB - Given a function f in the class C^(1,1)B(0, r), where B(0, r) denotes a ball of radius r in a real Banach space E, we provide the definition of a positive extended real number c*(f ) defined through the function, that plays a role in the study of the sensitivity of the Argmin map of the perturbed function F_g (p, u) = f (u) − g(p, u). This number coincides with the number c_2(f ) introduced by Zolezzi (2003) if linear perturbations g(p, u) = are considered.

KW - condition number theory

KW - convex optimization

KW - sensitivity

KW - condition number theory

KW - convex optimization

KW - sensitivity

UR - http://hdl.handle.net/10807/15203

UR - http://www.sciencedirect.com/science/journal/0362546x/75/1

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DO - 10.1016/j.na.2011.07.061

M3 - Article

SN - 0362-546X

VL - 2012

SP - 37

EP - 45

JO - NONLINEAR ANALYSIS

JF - NONLINEAR ANALYSIS

ER -

Conditioning for optimization problems under general perturbations

Abstract

Keywords

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