On second-order Taylor expansion of critical values - Zurich Open Repository and Archive

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.

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.

Citations

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Item Type: Journal Article, refereed, original work 03 Faculty of Economics > Department of Business Administration 330 Economics English 2010 12 Jul 2010 15:22 05 Apr 2016 14:10 Praha 0023-5954 http://www.kybernetika.cz/content/2010/3/472