TOMS450
Rosenbrock Function Minimization

TOMS450 is a FORTRAN77 library 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: http://www.acm.org/pubs/calgo or NETLIB: http://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.

Languages:

TOMS450 is available in a FORTRAN77 version.

Related Data and Programs:

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.

Examples and Tests:

• toms450_prb.f, a sample calling program.
• toms450_prb.sh, commands to compile and run the sample program.
• toms450_prb_output.txt, the output file.

List of Routines:

• ROMIN carries out Rosenbrock minimization of a scalar function of N variables.

You can go up one level to the FORTRAN77 source codes.