Abstract
We propose a technique of improving the dual estimates in nonconvex multiextremal problems of mathematical programming, by adding some additional constraints which are the consequences of the original constraints. This technique is used for the problems of finding the global minimum of polynomial functions, and extremal quadratic and boolean quadratic problems. In the article one ecological multiextremal problem and an algorithm for finding the dual estimate for it also considered. This algorithm is based upon a scheme of decomposition and nonsmooth optimization methods.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Artin, E. (1927), Ueber die Zerlegung definiter Funktionen in Quadrate, Hamburg Abh. N5, 100–15.
Hilbert, D. (1888), Ueber die Darstellung definiter Formen als Summen von Formen quadraten, Mathematical Annals 22, 342–350.
Pardalos, P. M. and J. B.Rosen (1987), Constrained Global Optimization: Algorithms and Applications, Lecture Notes in Computer Science 268, Springer-Verlag, New York.
Polya, G. (1928), Ueber positive Darstellung von Polynomen, Vierteljahrsschrift d. naturforschenden Gesellsch. Zürich 73, 141–145.
Shor, N. Z. (1985), Minimization Methods for Non-Differentiable Functions, Springer-Verlag, Berlin.
Shor, N. Z. (1987), Quadratic Optimization Problems, Izvestia of Academy of Sciences of USSR, Technical Cybernetics Moscow N1, 128–139 (in Russian).
Shor, N. Z. (1987), One Idea of Getting Global Extremum in Polynomial Problems of Mathematical Programming, Kibernetica 26 (5) 102–106, (in Russian).
Shor, N. Z. (1987), One Class of Estimates for Global Minimum of Polynomial Functions, Kibernetika 26 (6), 9–11 (in Russian).
Shor, N. Z. and S.I.Stetsenko (1989), Quadratic Extremal Problems and Nondifferentiable Optimization, Naukova Dumka, Kiev, 200 pp. (in Russian).
Lovasz, L. (1979), On the Shannon Capacity of a Graph, IEEE Transactions on Information Theory 25, 1–7.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shor, N.Z. Dual estimates in multiextremal problems. J Glob Optim 2, 411–418 (1992). https://doi.org/10.1007/BF00122430
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00122430