BRENT
Algorithms for Minimization Without Derivatives

BRENT is a FORTRAN77 library, using double precision arithmetic, which contains Richard Brent's algorithms for finding zeros or minima of a function, without requiring the use of derivatives (or assuming that the function is differentiable.)

Related Data and Programs:

ASA047 is a FORTRAN77 library which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

BRENT is also available in a C++ version and a C version and a FORTRAN90 version and a MATLAB version.

COORDINATE_SEARCH is a MATLAB program which minimizes a scalar function of several variables using the coordinate search algorithm.

GSL is the Gnu Scientific Library, a C++ library which includes rootfinding routines.

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

NMS is a FORTRAN90 library which includes versions of Brent's minimizer and zero finder.

PRAXIS is a FORTRAN77 library which minimizes a scalar function of several variables.

SLATEC is a FORTRAN90 library which includes the zero finder FZERO.

TEST_OPT a FORTRAN90 library which defines test problems requiring the minimization of a scalar function of several variables.

TEST_ZERO is a FORTRAN90 library which defines some test functions for which zeroes can be sought.

TOMS178 a FORTRAN77 library which optimizes a scalar functional of multiple variables using the Hooke-Jeeves method.

ZOOMIN is a FORTRAN90 library which includes various zero finder routines.

Reference:

1. Richard Brent,
   Algorithms for Minimization without Derivatives,
   Dover, 2002,
   ISBN: 0-486-41998-3,
   LC: QA402.5.B74.

Source Code:

• brent.f, the source code.
• brent.csh, commands to compile the source code.

Examples and Tests:

• brent_prb.f, a sample calling program.
• brent_prb.csh, commands to compile and run the sample program.
• brent_prb_output.txt, the output file.

List of Routines:

• GLOMIN seeks a global minimum of a function F(X) in an interval [A,B].
• LOCALM seeks a local minimum of a function F(X) in an interval [A,B].
• LOCAL_MIN_RC seeks a minimizer of a scalar function of a scalar variable.
• R8_EPSILON returns the R8 roundoff unit.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.
• ZERO seeks the root of a function F(X) in an interval [A,B].

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