Geodesic
On second–order Taylor expansion of critical values
Kybernetika, Tome 46 (2010) no. 3, pp. 472-487

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 49J52, 49K40, 65K05, 65K10, 90C30, 90C31
Keywords: Taylor expansion; parametric programs; critical value function; generalized derivatives; envelope theorems; Lipschitz stability; $C^{1, 1}$ optimization 
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     title = {On second{\textendash}order {Taylor} expansion of critical values},
     journal = {Kybernetika},
     pages = {472--487},
     publisher = {mathdoc},
     volume = {46},
     number = {3},
     year = {2010},
     mrnumber = {2676084},
     zbl = {1197.65062},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010__46_3_a11/}
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Bütikofer, Stephan; Klatte, Diethard; Kummer, Bernd. On second–order Taylor expansion of critical values. Kybernetika, Tome 46 (2010) no. 3, pp. 472-487. http://geodesic.mathdoc.fr/item/KYB_2010__46_3_a11/