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Optimum Seeking Methods (single variable)

  • Loo-Keng Hua
  • Yuan Wang
  • J. G. C. Heijmans
Part of the Mathematical Modeling book series (MMO, volume 2)

Abstract

An optimum seeking method (optimal search method, You Xuan Fa in Chinese) is a method to find technological production processes that are best in some sense, while using as few experiments as possible. It is a scientific method for arranging experiments. From our contacts with a large number of industries over the long period from 1970 to 1982, we have learned that this topic offers some of the most appropriate techniques for popularization.

Keywords

Maximum Point Unimodal Function Bisection Method Trial Point Fibonacci Sequence 
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.

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References

  1. Hua Loo Keng. Popular Lectures on Optimum Seekin Methods. Science Press, Beijing, 1971.Google Scholar
  2. Hua Loo Keng. Popular Lectures on Optimum Seekin Methods (with Supplements). Guo-Fang Industry Press, Beijing, 1973.Google Scholar
  3. Hua Loo Keng. Some Popular Lectures on Optimum Seekin Methods. Liao Ning People Press, Liao Ning, 1973.Google Scholar
  4. Hua Loo Keng. Theory of Optimization. Science Press, Beijing, 1981.Google Scholar
  5. Hua Loo Keng, Chen De Quan, Ji Lei etc (edited). A Collection of Literatures on Overall Planning Methods. Chinese Univ. of Science and Tech. Press, 1965.Google Scholar
  6. Kiefer J. “Sequential Minimax Search for a Maximum” Proc. Amer. Math.Soc, 4, 1953, pp. 502–506.MathSciNetMATHCrossRefGoogle Scholar
  7. Wilde, D.J. Optimum seeking Methods. Prentice Hall, N.J., 1964.Google Scholar
  8. Wu Fang. “Extremum of a Special Function” Scientia Sinica, 1, 1974, pp. 1–14.Google Scholar
  9. Editor’s note: Some additional references for this area are the following. Avriel, M. Nonlinear Programming: Analysis and Methods. Prentice-Hall, 1976.Google Scholar
  10. Bazaraa M.S., and C.M. Shetty. Nonlinear Programming. John Wiley & Sons, 1979.Google Scholar
  11. Beightle C.S., D.T. Phillips and D.J. Wilde. Foundations of Optimization. 2nd ed., Prentice-Hall, 1979.Google Scholar
  12. Kowalik J., and M.R. Osborne. “Methods for Unconstrained Optimization Problems” in Modern Analytic and Computational Methods, ed. R. Bellman. Am. Elsevier Publ. Comp., N.Y. 1968.Google Scholar
  13. Press, W.H., B.P. Flannery, S.A. Teukolsky and W.T. Vetterling. Numerical Recipes. Cambridge University Press, 1986.Google Scholar
  14. Scales, L.E. Introduction to Non-Linear Optimization. Springer 1985.Google Scholar

Copyright information

© Birkhäuser Boston 1989

Authors and Affiliations

  • Loo-Keng Hua
  • Yuan Wang
    • 1
  • J. G. C. Heijmans
    • 2
  1. 1.Academia SinicaInstitute of MathematicsBeijingPeople’s Republic of China
  2. 2.Department of MathematicsUniversity of Texas at ArlingtonArlingtonUSA

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