On second–order Taylor expansion of critical values

Stephan Bütikofer; Diethard Klatte; Bernd Kummer

Kybernetika (2010)

  • Volume: 46, Issue: 3, page 472-487
  • ISSN: 0023-5954

Abstract

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Studying a critical value function ϕ in parametric nonlinear programming, we recall conditions guaranteeing that ϕ 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 ϕ . 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.

How to cite

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Bütikofer, Stephan, Klatte, Diethard, and Kummer, Bernd. "On second–order Taylor expansion of critical values." Kybernetika 46.3 (2010): 472-487. <http://eudml.org/doc/196690>.

@article{Bütikofer2010,
abstract = {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.},
author = {Bütikofer, Stephan, Klatte, Diethard, Kummer, Bernd},
journal = {Kybernetika},
keywords = {Taylor expansion; parametric programs; critical value function; generalized derivatives; envelope theorems; Lipschitz stability; $C^\{1,1\}$ optimization; Taylor expansion; parametric programs; critical value function; generalized derivatives; envelope theorems; Lipschitz stability; optimization},
language = {eng},
number = {3},
pages = {472-487},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On second–order Taylor expansion of critical values},
url = {http://eudml.org/doc/196690},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Bütikofer, Stephan
AU - Klatte, Diethard
AU - Kummer, Bernd
TI - On second–order Taylor expansion of critical values
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 3
SP - 472
EP - 487
AB - 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.
LA - eng
KW - Taylor expansion; parametric programs; critical value function; generalized derivatives; envelope theorems; Lipschitz stability; $C^{1,1}$ optimization; Taylor expansion; parametric programs; critical value function; generalized derivatives; envelope theorems; Lipschitz stability; optimization
UR - http://eudml.org/doc/196690
ER -

References

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