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Second order sensitivity analysis and asymptotic theory of parametrized nonlinear programs

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Abstract

In this paper we study second-order differential properties of an optimal-value functionϕ(x). It is shown that under certain conditionsϕ(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.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of South Africa, P.O. Box 392, 0001, Pretoria, South Africa

    Alexander Shapiro

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  1. Alexander Shapiro
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Shapiro, A. Second order sensitivity analysis and asymptotic theory of parametrized nonlinear programs. Mathematical Programming 33, 280–299 (1985). https://doi.org/10.1007/BF01584378

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  • DOI: https://doi.org/10.1007/BF01584378

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