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Generalized descent for global optimization. (English) Zbl 0431.49036


MSC:

90C99 Mathematical programming
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[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 · doi:10.1287/mnsc.18.11.687
[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 · doi:10.1137/0714019
[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 · doi:10.1147/rd.165.0504
[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 · doi:10.1016/0304-4068(76)90019-7
[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 · doi:10.1007/BF01449146
[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 · doi:10.1137/0716057
[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.
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