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Second order sensitivity analysis and asymptotic theory of parametrized nonlinear programs. (English) Zbl 0579.90088

Summary: We study second-order differential properties of an optimal-value function \(\phi\) (x). It is shown that under certain conditions \(\phi\) (x) possesses second-order directional derivatives, which can be calculated by solving corresponding quadratic programs. Also upper and lower bounds on these derivatives are introduced under weaker assumptions. In particular we show that the second-order directional derivative is infinite if the corresponding quadratic program is unbounded. Finally sensitivity results are applied to investigate asymptotics of estimators in parametrized nonlinear programs.

MSC:

90C31 Sensitivity, stability, parametric optimization
90C30 Nonlinear programming
49M37 Numerical methods based on nonlinear programming
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