| Title:
|
On second–order Taylor expansion of critical values (English) |
| Author:
|
Bütikofer, Stephan |
| Author:
|
Klatte, Diethard |
| Author:
|
Kummer, Bernd |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
46 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
472-487 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Studying a critical value function $\varphi$ in parametric nonlinear programming, we recall conditions guaranteeing that $\varphi$ is a $C^{1,1}$ function and derive second order Taylor expansion formulas including second-order terms in the form of certain generalized derivatives of $D \varphi$. Several specializations and applications are discussed. These results are understood as supplements to the well–developed theory of first- and second-order directional differentiability of the optimal value function in parametric optimization. (English) |
| Keyword:
|
Taylor expansion |
| Keyword:
|
parametric programs |
| Keyword:
|
critical value function |
| Keyword:
|
generalized derivatives |
| Keyword:
|
envelope theorems |
| Keyword:
|
Lipschitz stability |
| Keyword:
|
$C^{1,1}$ optimization |
| MSC:
|
49J52 |
| MSC:
|
49K40 |
| MSC:
|
65K05 |
| MSC:
|
65K10 |
| MSC:
|
90C30 |
| MSC:
|
90C31 |
| idZBL:
|
Zbl 1197.65062 |
| idMR:
|
MR2676084 |
| . |
| Date available:
|
2010-09-13T16:58:25Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140762 |
| . |
| Reference:
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