DOI: 10.1007/bf01096413. Decomposition and interval arithmetic applied to global minimization of polynomial and rational functions

Decomposition and interval arithmetic applied to global minimization of polynomial and rational functions

10.1007/bf01096413

Crossref journal-article

Springer Science and Business Media LLC

Journal of Global Optimization (297)

Bibliography

Hansen, P., Jaumard, B., & Xiong, J. (1993). Decomposition and interval arithmetic applied to global minimization of polynomial and rational functions. Journal of Global Optimization, 3(4), 421â437.

Authors 3

Pierre Hansen (first)
Brigitte Jaumard (additional)
Junjie Xiong (additional)

References 16 Referenced 10

Alefeld, G. (1981), Bounding the Slope of Polynomial Operators and Some Applications,Computing 26, 227?237. (10.1007/BF02243480) / Computing by G. Alefeld (1981)
Cornelius, H. and R. Lohner, (1984), Computing the Range of Values of Real Functions with Accuracy Higher Than Second Order,Computing 33, 331?347. (10.1007/BF02242276) / Computing by H. Cornelius (1984)
Dixon, L. C. W. (1990), On Finding the Global Minimum of a Function of One Variable, Presented at the SIAM National Meeting, Chicago.
Dixon, L. C. W. and G. P. Szegõ (1975),Towards Global Optimization, North Holland, Amsterdam. / Towards Global Optimization by L. C. W. Dixon (1975)
Floudas, C. A. and V. Visweswaran (1990), A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs ? I. Theory,Computers and Chemical Engineering 14, 1397?1417. (10.1016/0098-1354(90)80020-C) / Computers and Chemical Engineering by C. A. Floudas (1990)
Floudas, C. A. and V. Visweswaran (1993), A Primal-Relaxed Dual Optimization Approach,Journal of Optimization Theory and Applications (to appear). (10.1007/BF00939667)
Goldstein, A. A. and J. F. Price (1971), On Descent from Local Minima,Mathematics of Computation 25, 569?574. (10.1090/S0025-5718-1971-0312365-X) / Mathematics of Computation by A. A. Goldstein (1971)
Hansen, P., Jaumard, B., and J. Xiong (1993), The Cord-Slope Form of Taylor's Expansion in Univariate Global Optimization,Journal of Optimization Theory and Applications (to appear). (10.1007/BF02207774)
Hansen, P. and B. Jaumard (1992), Reduction of Indefinite Quadratic Programs to Bilinear Programs,Journal of Global Optimization 2, 41?60. (10.1007/BF00121301) / Journal of Global Optimization by P. Hansen (1992)
Moore, R. (1966),Interval Analysis, Prentice-Hall, Englewood Cliffs, New Jersey. / Interval Analysis by R. Moore (1966)
Ratschek, H. and J. Rokne (1984),Computer Methods for the Range of Functions, Chichester, Ellis Horwood. / Computer Methods for the Range of Functions by H. Ratschek (1984)
Ratschek, H. and J. Rokne (1988),New Computer Methods for Global Optimization, Chichester, Ellis Horwood. / New Computer Methods for Global Optimization by H. Ratschek (1988)
Visweswaran, V. and C. A. Floudas (1990), A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs ? II, Application of Theory and Test Problems,Computers and Chemical Engineering 14, 1419?1434. (10.1016/0098-1354(90)80021-3) / Computers and Chemical Engineering by V. Visweswaran (1990)
Visweswaran, V. and C. A. Floudas (1992), Global Optimization of Problems with Polynomial Functions in One Variable, inRecent Advances in Global Optimization, pp. 165?199, Floudas, C. A. and Pardalos, P. M. (eds.), Princeton, Princeton University Press. / Recent Advances in Global Optimization by V. Visweswaran (1992)
Wilkinson, J. H. (1963),Rounding Errors in Algebraic Processes, Prentice-Hall, Englewood Cliffs, New Jersey. / Rounding Errors in Algebraic Processes by J. H. Wilkinson (1963)
Wingo, D. R. (1985), Globally Minimizing Polynomials without Evaluating Derivatives,International Journal of Computer Mathematics 17, 287?294. (10.1080/00207168508803469) / International Journal of Computer Mathematics by D. R. Wingo (1985)

Dates

Type	When
Created	20 years, 6 months ago (Feb. 5, 2005, 4:15 a.m.)
Deposited	5 years, 4 months ago (April 5, 2020, 11:59 a.m.)
Indexed	1 month, 4 weeks ago (July 1, 2025, 7:06 a.m.)
Issued	32 years, 8 months ago (Jan. 1, 1993)
Published	32 years, 8 months ago (Jan. 1, 1993)
Published Print	32 years, 8 months ago (Jan. 1, 1993)

Funders 0

None

BibTeX

@article{Hansen_1993, title={Decomposition and interval arithmetic applied to global minimization of polynomial and rational functions}, volume={3}, ISSN={1573-2916}, url={http://dx.doi.org/10.1007/bf01096413}, DOI={10.1007/bf01096413}, number={4}, journal={Journal of Global Optimization}, publisher={Springer Science and Business Media LLC}, author={Hansen, Pierre and Jaumard, Brigitte and Xiong, Junjie}, year={1993}, pages={421–437} }

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