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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; $C^{1,1}$ optimization
Summary:
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.
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