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Quasidifferentiability and Related Topics pp 139–149Cite as

On Directional Differentiability of Marginal Functions in Quasidifferentiable Case

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Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 43))

Abstract

Sufficient conditions of directional differentiability of marginal functions defined by quasidifferentiable functions, are obtained. The result is adapted for the distance function to a quasidifferentiable set.

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References

  • Demyanov, V.F., Rubinov, A.M. (1995), Constructive Nonsmooth Analysis, Peter Lang Verlag, Frankfurt a/M.

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  • Minchenko, L.I, Borisenko, O.F and Grizai, S.P (1993), Set-Valued Analysis and Perturbed Problems of Nonlinear Programming, Naukai Technika, Minsk. (In Russian)

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  • Demyanov, V.F and Zabrodin, LS. (1986), Directional Differentiability of a Continual Maximum Function of Quasidifferentiable Functions, Mathematical Programming Study, Vol. 29, pp. 108–117.

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  • Demyanov, V.F. and Vasiliev, L.V. (1985), Nondifferentiable Optimization, Springer Optimization Software, New York.

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  • Pschenichnyi B.N. (1980), Convex Analysis and Extremal Problems, Nauka, Moscow. (In Russian)

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  • Dudov, S.I. (1995), Directional Differentiability of the Distance Function, Matematicheskii Sbornik, Vol. 186, No 3, pp. 29–52. (In Russian)

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  • Ioffe, A.D. and Tikhomirov, V.M. (1979), Theory of Extremal Problems, North Holland, Amsterdam.

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Author information

Authors and Affiliations

  1. Department of Mechanics and Mathematics, Saratov State University, Astrahanskaya, 83, 410026, Saratov, Russia

    Sergey I. Dudov

Authors
  1. Sergey I. Dudov
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Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, St. Petersburg State University, St. Petersburg, Russia

    Vladimir Demyanov

  2. School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria, Australia

    Alexander Rubinov

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© 2000 Springer Science+Business Media Dordrecht

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Dudov, S.I. (2000). On Directional Differentiability of Marginal Functions in Quasidifferentiable Case. In: Demyanov, V., Rubinov, A. (eds) Quasidifferentiability and Related Topics. Nonconvex Optimization and Its Applications, vol 43. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3137-8_5

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  • DOI: https://doi.org/10.1007/978-1-4757-3137-8_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4830-4

  • Online ISBN: 978-1-4757-3137-8

  • eBook Packages: Springer Book Archive

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