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Nonsmooth Optimization and Related Topics pp 167–183Cite as

Directional Derivative for the Value Function in Mathematical Programming

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Part of the book series: Ettore Majorana International Science Series ((EMISS,volume 43))

Abstract

The conditions for the existence of the directional derivative of the optimal value function in mathematical programming is a difficult question still not completely solved. Here we study a case where the directional derivative is obtained with a nice formula when some corresponding optimal solutions have Lipschitzian or Hölderian directional behaviour. These calm properties for optimal solutions are obtained with near to minimal assumptions and regularity conditions (constraints qualification) as illustrated by examples.

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References

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Author information

Authors and Affiliations

  1. Dept. de Mathématiques Appliquées, École Polytechnique, Univ. de Montréal, Montréal, Quebec, Canada

    J. Gauvin

Authors
  1. J. Gauvin
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Editor information

Editors and Affiliations

  1. Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succ.A, H3C 3J7, Montréal, Quebec, Canada

    F. H. Clarke

  2. Department of Applied Mathematics, Leningrad State University, Staryi Peterhof, 198904, Leningrad, USSR

    V. F. Dem’yanov

  3. Dipartimento di Mathematica, Universitá di Pisa, Via F. Buonarroti 2, 56100, Pisa, Italy

    F. Giannessi

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© 1989 Springer Science+Business Media New York

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Gauvin, J. (1989). Directional Derivative for the Value Function in Mathematical Programming. In: Clarke, F.H., Dem’yanov, V.F., Giannessi, F. (eds) Nonsmooth Optimization and Related Topics. Ettore Majorana International Science Series, vol 43. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6019-4_11

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  • DOI: https://doi.org/10.1007/978-1-4757-6019-4_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-6021-7

  • Online ISBN: 978-1-4757-6019-4

  • eBook Packages: Springer Book Archive

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