Given a function f∈C1,1(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 ĉ(f) defined through the function, that plays a role in the study of the sensitivity of the Argmin map of the perturbed function Fg(p,u)=f(u)-g(p,u). This number coincides with the number c2(f) introduced by Zolezzi (2003) if linear perturbations g(p,u)=〈p,u〉 are considered. © 2011 Elsevier Ltd. All rights reserved.

Bianchi, M., Kassay, G., Pini, R. (2012). Conditioning for optimization problems under general perturbations. NONLINEAR ANALYSIS, 75(1), 37-45 [10.1016/j.na.2011.07.061].

Conditioning for optimization problems under general perturbations

PINI, RITA
2012

Abstract

Given a function f∈C1,1(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 ĉ(f) defined through the function, that plays a role in the study of the sensitivity of the Argmin map of the perturbed function Fg(p,u)=f(u)-g(p,u). This number coincides with the number c2(f) introduced by Zolezzi (2003) if linear perturbations g(p,u)=〈p,u〉 are considered. © 2011 Elsevier Ltd. All rights reserved.
Articolo in rivista - Articolo scientifico
Condition number theorem, sensitivity, convex optimization
English
2012
75
1
37
45
none
Bianchi, M., Kassay, G., Pini, R. (2012). Conditioning for optimization problems under general perturbations. NONLINEAR ANALYSIS, 75(1), 37-45 [10.1016/j.na.2011.07.061].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/26520
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