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  • Global optimization  (2)
  • Storm's chain  (1)
  • rational functions  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Simple global minimization algorithm for one-variable rational functions (1995)
    Springer
    Journal of global optimization 6 (1995), S. 293-311 
    Details
    ISSN: 1573-2916
    Keywords: Global optimization ; univariate optimization ; polynomials ; rational functions ; Storm's chain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Sturm's chain technique for evaluation of a number of real roots of polynomials is applied to construct a simple algorithm for global optimization of polynomials or generally for rational functions of finite global minimal value. The method can be applied both to find the global minimum in an interval or without any constraints. It is shown how to use the method to minimize globally a truncated Fourier series. The results of numerical tests are presented and discussed. The cost of the method scales as the square of the degree of the polynomial.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01099466
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Diffusion equation method of global minimization: Performance for standard test functions (1991)
    Springer
    Journal of optimization theory and applications 69 (1991), S. 269-284 
    Details
    ISSN: 1573-2878
    Keywords: Global optimization ; global minimum ; diffusion ; multiple minima
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently, we have proposed a method of global minimization that is based on solving the diffusion equation with the objective function as a boundary condition. In the present paper, the performance of the method is examined when applied to the standard test functions of the Goldstein-Price, Hartman, Shekel, and Griewank families. It turns out that the method succeeds in all these cases. A comparison of the effectiveness of our method and other methods is also reported.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940643
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