Algorithms for Minimization Without Derivatives

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Courier Dover Publications, 1973 - Computers - 195 pages
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This outstanding text for graduate students and researchers proposes improvements to existing algorithms, extends their related mathematical theories, and offers details on new algorithms for approximating local and global minima. None of the algorithms requires an evaluation of derivatives; all depend entirely on sequential function evaluation, a highly practical scenario in the frequent event of difficult-to-evaluate derivatives.
Topics include the use of successive interpolation for finding simple zeros of a function and its derivatives; an algorithm with guaranteed convergence for finding a minimum of a function of one variation; global minimization given an upper bound on the second derivative; and a new algorithm for minimizing a function of several variables without calculating derivatives. Many numerical examples augment the text, along with a complete analysis of rate of convergence for most algorithms and error bounds that allow for the effect of rounding errors.
  

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Contents

SOME USEFUL RESULTS ON TAYLOR SERIES
9
THE USE OF SUCCESSIVE INTERPOLATION
19
AN ALGORITHM WITH GUARANTEED
47
AN ALGORITHM WITH GUARANTEED
61
GLOBAL MINIMIZATION GIVEN AN UPPER
81
A NEW ALGORITHM FOR MINIMIZING
116
BIBLIOGRAPHY
169
FORTRAN subroutines
187
INDEX
193
Copyright

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About the author (1973)

Richard Brent is a Professor of Mathematics and Computer Science at the Australian National University, Canberra.

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