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On second-order Taylor expansion of critical values


Bütikofer, S; Klatte, D; Kummer, B (2010). On second-order Taylor expansion of critical values. Kybernetika, 46(3):472-487.

Abstract

Studying a critical value function $\vi$ in parametric nonlinear programming, we recall conditions guaranteeing that $\vi$ 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 $D \vi$. 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.

Studying a critical value function $\vi$ in parametric nonlinear programming, we recall conditions guaranteeing that $\vi$ 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 $D \vi$. 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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Business Administration
Dewey Decimal Classification:330 Economics
Language:English
Date:2010
Deposited On:12 Jul 2010 15:22
Last Modified:05 Apr 2016 14:10
Publisher:Praha
ISSN:0023-5954
Official URL:http://www.kybernetika.cz/content/2010/3/472
Permanent URL: https://doi.org/10.5167/uzh-34745

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