On second-order Taylor expansion of critical values

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.