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Nonsmooth Optimization and Dual Bounds

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Nonsmooth Optimization and Related Topics

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

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Abstract

Lagrange function is a source for getting so called “dual bounds” for a wide class of mathematical programming problems: to find

$$f* = \inf {f_o}\left( x \right);X \subseteq {\mathbb{R}^n}$$
(1)

; subject to the constraints:

$${f_i}\left( x \right) \leqslant 0,i = 1, \ldots ,m$$
(2)

.

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References

  1. N.Z. Shor. “Minimization methods for non-differentiable functions”. Springer-Verlag (1985).

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  2. V.S. Michalevich, V.A. Trubin, N.Z. Shor. “Mathematical methods for solving optimization problems of production”. Transport planning, Moscow, Nauka (1986), (in Russian).

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  3. N.Z. Shor. “Quadratic optimization problems”. Izvestia of AN USSR. Technical Cybernetics, Moscow, N. 1 (1987), pp. 128–139.

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  4. N.Z. Shor. “One idea of getting global extremus in polynomial problems of mathematical programming”. Kibernetica, Kiev, N. 5 (1987), pp. 102–106.

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  5. N.Z. Shor. “One class estimates of global minimum of polynomial functions”. Kibernetica, Kiev, N. 6 (1987), pp. 9–11.

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  6. D. Hilbert. “Uber die darstellung definiter Formen als Summen von Formen quadraten”. Math. Ann., Vol. 22 (1888), pp. 342–350.

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  7. L. Lovasz. “On the Shannon capacity of a graph”. IEEE Trans. Inform. Theory (1979), T-25,M.

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  8. N.Z. Shor, S. I. Stecenko. “Quadratic Boolean problems and Lovasz’s bounds”. Abstract IFIP Conference, Budapest (1985).

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Author information

Authors and Affiliations

  1. V.M. Glushkov Institute of Cybernetics, Kiev, USSR

    N. Z. Shor

Authors
  1. N. Z. Shor
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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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Shor, N.Z. (1989). Nonsmooth Optimization and Dual Bounds. 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_23

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  • DOI: https://doi.org/10.1007/978-1-4757-6019-4_23

  • 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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