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Nonsmooth analysis and parametric optimization

Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 1446)

Abstract

In an optimization problem that depends on parameters, an important issue is the effect that perturbations of the parameters can have on solutions to the problem and their associated multipliers. Under quite broad conditions the possibly multi-valued mapping that gives these elements in terms of the parameters turns out to enjoy a property of “proto-differentiability.” Generalized derivatives can then be calculated by solving an auxiliary optimization problem with auxiliary parameters. This is constructed from the original problem by taking second-order epi-derivatives of an essential objective function.

Keywords

  • Tangent Cone
  • Constraint Qualification
  • Finite Dimension
  • Nonsmooth Analysis
  • Reflexive Banach Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work was supported in part by the National Science Foundation at the University of Washington, Seattle

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© 1990 Springer-Verlag

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Rockafellar, R.T. (1990). Nonsmooth analysis and parametric optimization. In: Cellina, A. (eds) Methods of Nonconvex Analysis. Lecture Notes in Mathematics, vol 1446. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084934

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  • DOI: https://doi.org/10.1007/BFb0084934

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