TY - JOUR
T1 - Conditioning for optimization problems under general perturbations
AU - Bianchi, Monica
AU - Pini, Rita
AU - Kassay, G.
AU - Pini, R.
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
U2 - 10.1016/j.na.2011.07.061
DO - 10.1016/j.na.2011.07.061
M3 - Article
VL - 2012
SP - 37
EP - 45
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
ER -