toms450

toms450, a Fortran77 code which implements ACM toms algorithm 450, for seeking the minimizer of a scalar function of N variables.

The text of the algorithm as printed in the original reference had a number of errors which were corrected in a remark made the following year. The text of the algorithm has been corrected accordingly.

The text of many ACM TOMS algorithms is available online through ACM: https://www.acm.org/pubs/calgo or NETLIB: https://www.netlib.org/toms/index.html.

Usage:

call romin ( n, x, funct, step, monitr )

where N is the number of variables, x is the estimated minimizer, funct is an external subroutine for evaluating the function, step is a stepsize, and monitr is a user routine which determines when to declare convergence.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

toms450 is available in a Fortran77 version.

Related Data and Programs:

toms450_test

minpack, a Fortran90 library which contains routines which can minimize the absolute value of a function of several variables.

TEST_OPT, a Fortran90 library which contains routines defining a number of scalar functions of multiple variables to test minimization routines.

Reference:

1. Marek Machura, Andrzej Mulawa,
   Algorithm 450: Rosenbrock Function Minimization,
   Communications of the ACM,
   August 1973, Volume 16, Number 8, pages 482-483.
2. Adhemar Bulktheel,
   Remark on Algorithm 450: Rosenbrock Function Minimization,
   Communications of the ACM,
   August 1974, Volume 17, Number 8, page 470.

Source Code:

• toms450.f, the source code.
• toms450.sh, commands to compile the source code.