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 the poorest value. The process is adaptive, causing the simplexes to be continually revised to best conform to the nature of the response surface. The generality of the method is illust'rated by using it. to solve six problems appearing in the May 1973 issue of Technometrics.

[1]  E. S. Pearson,et al.  TABLES OF PERCENTAGE POINTS OF THE INVERTED BETA (F) DISTRIBUTION , 1943 .

[2]  R. Ryhage,et al.  High-speed Computers as a Supplement to Graphical Methods. III. Twist Matrix Methods for Minimizing the Error-square Sum in Problems with Many Unknown Constants. , 1962 .

[3]  G. R. Hext,et al.  Sequential Application of Simplex Designs in Optimisation and Evolutionary Operation , 1962 .

[4]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[5]  S. D. Christian.  Graphical least squares analysis , 1965 .

[6]  Richard R. Ernst,et al.  Measurement and Control of Magnetic Field Homogeneity , 1968 .

[7]  E. A. Sylvestre,et al.  Elimination of Linear Parameters in Nonlinear Regression , 1971 .

[8]  R. O'Neill.  Algorithm AS 47: Function Minimization Using a Simplex Procedure , 1971 .

[9]  Empirical Equations for Approximating Tabular F Values , 1973 .

[10]  Nozer D. Singpurwalla,et al.  Inference from Accelerated Life Tests Using Arrhenius Type Re-Parameterizations , 1973 .

[11]  V. Pereyra,et al.  Least Squares Estimation for a Class of Non-Linear Models , 1973 .

[12]  Estimation in Compound Exponential Failure Models–When the Data are Grouped , 1973 .

[13]  R. H. Myers,et al.  Response Surface Techniques for Dual Response Systems , 1973 .

[14]  D. Keefer.  Simpat: Self-Bounding Direct Search Method for Optimization , 1973 .

[15]  G. Richard Atwood,et al.  Transformation of Bounded Variables in Simplex Optimization Techniques , 1973 .

[16]  H. Britt,et al.  The Estimation of Parameters in Nonlinear, Implicit Models , 1973 .

[17]  Helen J. Mikulski,et al.  Statistical Computer Programs: A Sequential Simplex Program for Solving Minimization Problems , 1974 .