Abstract
Lagrange function is a source for getting so called “dual bounds” for a wide class of mathematical programming problems: to find
; subject to the constraints:
.
Keywords
- Lagrange Function
- Quadratic Constraint
- Quadratic Problem
- Nonsmooth Optimization
- Quadratic Optimization Problem
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N.Z. Shor. “Minimization methods for non-differentiable functions”. Springer-Verlag (1985).
V.S. Michalevich, V.A. Trubin, N.Z. Shor. “Mathematical methods for solving optimization problems of production”. Transport planning, Moscow, Nauka (1986), (in Russian).
N.Z. Shor. “Quadratic optimization problems”. Izvestia of AN USSR. Technical Cybernetics, Moscow, N. 1 (1987), pp. 128–139.
N.Z. Shor. “One idea of getting global extremus in polynomial problems of mathematical programming”. Kibernetica, Kiev, N. 5 (1987), pp. 102–106.
N.Z. Shor. “One class estimates of global minimum of polynomial functions”. Kibernetica, Kiev, N. 6 (1987), pp. 9–11.
D. Hilbert. “Uber die darstellung definiter Formen als Summen von Formen quadraten”. Math. Ann., Vol. 22 (1888), pp. 342–350.
L. Lovasz. “On the Shannon capacity of a graph”. IEEE Trans. Inform. Theory (1979), T-25,M.
N.Z. Shor, S. I. Stecenko. “Quadratic Boolean problems and Lovasz’s bounds”. Abstract IFIP Conference, Budapest (1985).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer Science+Business Media New York
About this chapter
Cite this chapter
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
Download citation
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