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Griewank, A. O.

Generalized descent for global optimization. (English) Zbl 0431.49036

J. Optimization Theory Appl. 34, 11-39 (1981).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0431.49036

Cited in 1 Review
Cited in 45 Documents

MSC:

90C99 Mathematical programming

Keywords:

global optimization; generalized descent; search trajectories; target level
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\textit{A. O. Griewank}, J. Optim. Theory Appl. 34, 11--39 (1981; Zbl 0431.49036)
Full Text: DOI

Online Encyclopedia of Integer Sequences:

Value at which the smallest positive local minimum of the 1-D Griewank function occurs.

References:

[1] Schubert, B. O.,Sequential Optimization of Multimodal Discrete Function with Bounded Rate of Change, Management Science, Vol. 18, pp. 687-693, 1972. · Zbl 0241.90038
[2] Aird, T. J., andRice, J. R.,Systematic Search in High Dimensional Sets, SIAM Journal of Numerical Analysis, Vol. 14, pp. 296-312, 1977. · Zbl 0359.68044
[3] Dickson, L. C. W., Gomulka, J., andSzegö, G. P.,Toward a Global Optimization Technique, Toward Global Optimization, Edited by L. Dickson and G. Szegö, North-Holland Publishing Company, Amsterdam, Holland, 1975.
[4] Branin, F. H.,Widely Convergent Method for Finding Multiple Solutions of Nonlinear Equations, IBM Journal of Research and Development, Vol. 16, pp. 504-522, 1972. · Zbl 0271.65034
[5] Hirsch, M.,Differential Topology, Springer-Verlag, New York, New York, 1976.
[6] Smale, S.,A Convergent Process of Price Adjustment and Global Newton Methods, Journal of Mathematical Economics, Vol. 3, pp. 107-220, 1976. · Zbl 0354.90018
[7] Keller, H. B.,Global Homotopics and Newton Methods, Recent Advances in Numerical Analysis, Edited by C. DeBoor and G. H. Golub, Academic Press, New York, New York, 1978.
[8] John, F.,Ueber die Vollstaendigkeit der Relationen von Morse fuer die Anzahlen Kritischer Punkte, Mathematische Annalen, Vol. 109, pp. 381-394, 1934. · Zbl 0008.21301
[9] Griewank, A.,A Generalized Descent Method for Global Optimization, Australian National University, MS Thesis, 1977.
[10] Willmore, T. J.,An Introduction to Differential Geometry, Clarendon Press, Oxford, England, 1959. · Zbl 0086.14401
[11] Inomata, S., andCumada, M.,On the Golf Method, Denshi Gijutso Sogo Kenkyujo, Tokyo, Japan, Bulletin of the Electrotechnical Laboratory, Vol. 25, pp. 495-512, 1964.
[12] Zidkov, N. P., andSiedrin, B. M.,A Certain Method of Search for the Minimum of a Function of Several Variables, Computing Methods and Programming, Izdat Moscow University, Vol. 10, pp. 203-210, 1968.
[13] Incerti, S., Parisi, V., andZirilli, F.,A New Method for Solving Nonlinear Simultaneous Equations, SIAM Journal of Numerical Analysis, Vol. 16, pp. 779-789, 1979. · Zbl 0411.65028
[14] Griewank, A.,Analysis and Modification of Newton’s Method at Singularities, Australian National University, PhD Thesis, 1980. · Zbl 0419.65034
[15] Powell, M. J. D.,A New Algorithm for Unconstrained Optimization, Nonlinear Programming, Edited by J. B. Rosen, O. L. Mangasarian, and K. Ritter, Academic Press, New York, New York, 1970. · Zbl 0228.90043
[16] Gear, C. W.,Numerical Initial-Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1971. · Zbl 1145.65316
[17] Anonymous, International Mathematical and Statistical Libraries, Library 2, Edition 6, Vol. 1, Houston, Texas, 1977.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.