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
An improved simplex method for function minimization
  • Yuguang Huang, W. Mccoll
  • Computer Science
  • 1996 IEEE International Conference on Systems, Man and Cybernetics. Information Intelligence and Systems (Cat. No.96CH35929)
  • 1996
TLDR
An improved method based on Nelder and Mead's simplex method (1965) is described for unconstrained function minimization, which reflects a more reasonable descendant search nature of thesimplex method. Expand
A New Method of Constrained Optimization and a Comparison With Other Methods
A new method for finding the maximum of a general non-linear function of several variables within a constrained region is described, and shown to be efficient compared with existing methods when theExpand
The Nelder-Mead Simplex Procedure for Function Minimization
The Nelder-Mead simplex method for function minimization is a “direct” method requiring no derivatives. The objective function is evaluated at the vertices of a simplex, and movement is away from theExpand
Global Optimization for Imprecise Problems
A new method for the computation of the global minimum of a continuously differentiable real—valued function f of n variables is presented. This method, which is composed of two parts, is based onExpand
Location of saddle points and minimum energy paths by a constrained simplex optimization procedure
Two methods are proposed, one for the location of saddle points and one for the calculation of steepest-descent paths on multidimensional surfaces. Both methods are based on a constrained simplexExpand
Refined simplex fitting method
The simplex fitting method makes use of a geometrical figure that finds the minimum variance value in successive steps. It was developed from the idea of finding the minimum value of a function. AExpand
Lattice Approximations to the Minima of Functions of Several Variables
  • G. Berman
  • Mathematics, Computer Science
  • JACM
  • 1969
TLDR
A computer-oriented method is developed for determining relative minima of functions of several variables which always converges to a relative minimum no matter which initial point is used. Expand
Numerical optimization and surface estimation with imprecise function evaluations
TLDR
The present work attempts to classify both problems and algorithmic tools in an effort to prescribe suitable techniques in a variety of situations to minimize functions of several parameters where the function need not be computed precisely. Expand
THE SIMPLEX TECHNIQUE AS A GENERAL OPTIMIZATION METHOD
This paper first describes the classical simplex method and its most popular improvements, then it shows how this simplex procedure can be generalized to include the presence of constraints. TheExpand
Simplex Optimization and Its Applicability for Solving Analytical Problems
Formulation of the simplex matrix referred to n-D space, is presented in terms of the scalar product of vectors, known from elementary algebra. The principles of a simplex optimization procedureExpand
...
1
2
3
4
5
...

References

SHOWING 1-5 OF 5 REFERENCES
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
  • M. Powell
  • Mathematics, Computer Science
  • Comput. J.
  • 1962
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 inExpand