A direct search method of optimization that works moderately well for stochastic problems. It is based on evaluating a function at the vertices of a simplex, then iteratively shrinking the simplex as better points are found until some desired bound is obtained (Nelder and Mead 1965). The Nelder-Mead method is implemented as NMinimize[f, vars, Method -> "NelderMead"].
See alsoStochastic Optimization
ReferencesLagarias, J. C.; Reeds, J. A.; Wright, M. H.; and Wright, P. E. "Convergence Properties of the Nelder-Mead Algorithm in Low Dimensions." AT&T Bell Laboratories Tech. Rep. Murray Hill, NJ, 1995.Nelder, J. A. and Mead, R. "A Simplex Method for Function Minimization." Comput. J. 7, 308-313, 1965.Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, 1989.Walters, F. H.; Parker, L. R. Jr.; Morgan, S. L.; and Deming, S. N. Sequential Simplex Optimization: A Technique for Improving Quality and Productivity in Research, Development, and Manufacturing. Boca Raton, FL: CRC Press, 1991.Woods, D. J. An Interactive Approach for Solving Multi-Objective Optimization Problems. Ph.D. thesis. Houston, TX: Rice University, 1985.Wright, M. H. "The Nelder-Mead Method: Numerical Experimentation and Algorithmic Improvements." AT&T Bell Laboratories Techn. Rep. Murray Hill, NJ.Wright, M. H. "Direct Search Methods: Once Scorned, Now Respectable." In Numerical Analysis 1995. Papers from the Sixteenth Dundee Biennial Conference held at the University of Dundee, Dundee, June 27-30, 1995 (Ed. D. F. Griffiths and G. A. Watson). London: Longman, Harlow, pp. 191-208, 1996.
Referenced on Wolfram|AlphaNelder-Mead Method
Cite this as:
Weisstein, Eric W. "Nelder-Mead Method." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Nelder-MeadMethod.html