ASA047
Nelder-Mead Minimization Algorithm

ASA047 is a MATLAB library which seeks to minimize a scalar function of several variables using the Nelder-Mead algorithm, by R ONeill.

ASA047 is Applied Statistics Algorithm 47. Source code for many Applied Statistics Algorithms is available through STATLIB.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

ASA047 is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

COMPASS_SEARCH, a MATLAB library which seeks the minimizer of a scalar function of several variables using compass search, a direct search algorithm that does not use derivatives.

DQED, a FORTRAN90 library which solves constrained least squares problems.

ENTRUST, a MATLAB program which minimizes a scalar function of several variables using trust-region methods.

MINPACK, a FORTRAN90 library which solves systems of nonlinear equations, or the least squares minimization of the residual of a set of linear or nonlinear equations.

NELDER_MEAD, a MATLAB program which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

NL2SOL, a FORTRAN90 library which implements an adaptive nonlinear least-squares algorithm.

PRAXIS, a FORTRAN90 library which minimizes a scalar function of several variables.

TEST_OPT, a MATLAB library which defines test problems requiring the minimization of a scalar function of several variables.

TOMS178, a MATLAB library which optimizes a scalar functional of multiple variables using the Hooke-Jeeves method.

TOMS611, a FORTRAN77 library which solves problems in unconstrained minimization.

Author:

Original FORTRAN77 version by R ONeill; MATLAB version by John Burkardt.

Reference:

1. John Nelder, Roger Mead,
   A simplex method for function minimization,
   Computer Journal,
   Volume 7, 1965, pages 308-313.
2. R ONeill,
   Algorithm AS 47: Function Minimization Using a Simplex Procedure,
   Applied Statistics,
   Volume 20, Number 3, 1971, pages 338-345.

Source Code:

• nelmin.m minimizes a function using the Nelder-Mead algorithm.
• timestamp.m prints out the current YMDHMS date as a timestamp.

Examples and Tests:

• asa047_test.m, a sample calling program.
• asa047_test01.m, tests NELMIN with the Rosenbrock function.
• rosenbrock.m, evaluates the Rosenbrock function.
• asa047_test02.m, tests NELMIN with the Powell function.
• powell.m, evaluates the Powell function.
• asa047_test03.m, tests NELMIN with the helical function.
• helical.m, evaluates the helical function.
• asa047_test04.m, tests NELMIN with the quarrtic function.
• quartic.m, evaluates the quartic function.
• asa047_test_output.txt, the output file.

You can go up one level to the MATLAB source codes.