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ε-Quasidifferentiability of real-valued functions and optimality conditions in extremal problems

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Quasidifferential Calculus

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 29))

Abstract

In this paper we demonstrate how the concept of quasidifferentiability introduced by Demyanov and Rubinov may be extended to the more general concepts of ε-quasidifferentiability and approximate quasidifferentiability. We study the ε-quasidifferentiability of composite functions and present some rules for ε-quasidifferential calculus. The optimality conditions for some typical extremal problems are restated in terms of ε-quasidifferentials.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Byelorussian SSR, Surganov St. 11, 220604, Minsk, USSR

    V. V. Gorokhovik

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  1. V. V. Gorokhovik
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V. F. Demyanov L. C. W. Dixon

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© 1986 The Mathematical Programming Society, Inc.

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Gorokhovik, V.V. (1986). ε-Quasidifferentiability of real-valued functions and optimality conditions in extremal problems. In: Demyanov, V.F., Dixon, L.C.W. (eds) Quasidifferential Calculus. Mathematical Programming Studies, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121147

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  • DOI: https://doi.org/10.1007/BFb0121147

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00928-0

  • Online ISBN: 978-3-642-00929-7

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