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Sensitivity, Stability and Parametric Analysis pp 213–226Cite as

Directional differentiability of the optimal value function in a nonlinear programming problem

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Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 21))

Abstract

A parameterized nonlinear programming problem is considered in which the objective and constraint functions are twice continuously differentiable. Under the assumption that certain multiplier vectors appearing in generalized second-order necessary conditions for local optimality actually satisfy the weak sufficient condition for local optimality based on the augmented Lagrangian, it is shown that the optimal value in the problem, as a function of the parameters, is directionally differentiable. The directional derivatives are expressed by a minimax formula which generalizes the one of Gol’shtein in convex programming.

Research sponsored in part by the Air Force Office of Scientific Research, AFSC, United States Air Force, under grant no. F49620-82-K-0012.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, 98195, Seattle, WA, USA

    R. T. Rockafellar

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  1. R. T. Rockafellar
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Anthony V. Fiacco

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© 1984 The Mathematical Programming Society, Inc.

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Rockafellar, R.T. (1984). Directional differentiability of the optimal value function in a nonlinear programming problem. In: Fiacco, A.V. (eds) Sensitivity, Stability and Parametric Analysis. Mathematical Programming Studies, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121219

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  • DOI: https://doi.org/10.1007/BFb0121219

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00912-9

  • Online ISBN: 978-3-642-00913-6

  • eBook Packages: Springer Book Archive

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