A Simplex Method for Function Minimization

@article{Nelder1965ASM,
  title={A Simplex Method for Function Minimization},
  author={John A. Nelder and Roger Mead},
  journal={Comput. J.},
  year={1965},
  volume={7},
  pages={308-313}
}
A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. [...] Key Method The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.Expand
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  • Computer Science
  • 1996 IEEE International Conference on Systems, Man and Cybernetics. Information Intelligence and Systems (Cat. No.96CH35929)
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References

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A Rapidly Convergent Descent Method for Minimization
TLDR
A number of theorems are proved to show that it always converges and that it converges rapidly, and this method has been used to solve a system of one hundred non-linear simultaneous equations. Expand
An Iterative Method for Finding Stationary Values of a Function of Several Variables
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TLDR
An iterative method which is not unlike the conjugate gradient method of Hestenes and Stiefel (1952), and which finds stationary values of a general function, which has second-order convergence. Expand
Sequential Application of Simplex Designs in Optimisation and Evolutionary Operation
A technique for empirical optimisation is presented in which a sequence of experimental designs each in the form of a regular or irregular simplex is used, each simplex having all vertices but one in… Expand
An efficient method for finding the minimum of a function of several variables without calculating derivatives
An Automatic Method for Finding the Greatest or Least Value of a Function