ON SECOND-ORDER TAYLOR EXPANSION OF CRITICAL VALUES
Studying a critical value function phi in parametric nonlinear programming, we recall conditions guaranteeing that phi 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 phi. 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.
taylor expansion critical value function generalized derivatives parametric programs envelope theorems lipschitz stability c(1,1) optimization