Conditioning for optimization problems under general perturbations
Given a function f ∈ 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 ˆ ( f ) defined through the function, that plays a role in the study of the sensitivity of the Argmin map of the pertu...
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| Vydané v: | Nonlinear analysis Ročník 75; číslo 1; s. 37 - 45 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Amsterdam
Elsevier Ltd
2012
Elsevier |
| Predmet: | |
| ISSN: | 0362-546X, 1873-5215 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | Given a function
f
∈
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
ˆ
(
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. |
|---|---|
| Bibliografia: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 0362-546X 1873-5215 |
| DOI: | 10.1016/j.na.2011.07.061 |