BRENT
Algorithms for Minimization Without Derivatives

BRENT, a FORTRAN77 library which contains algorithms for finding zeros or minima of a scalar function of a scalar variable, by Richard Brent.

The methods do not require the use of derivatives, and do not assume that the function is differentiable.

Licensing:

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

Languages:

BRENT 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:

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

BISECTION_RC, a FORTRAN77 library which seeks a solution to the equation F(X)=0 using bisection within a user-supplied change of sign interval [A,B]. The procedure is written using reverse communication.

brent, a FORTRAN77 library which contains routines for finding zeroes or minima of a scalar function of a scalar variable, without the use of derivative information, including a reverse communication (RC) option, by Richard Brent.

brent_test

COMPASS_SEARCH, a FORTRAN90 library which seeks the minimizer of a scalar function of several variables using compass search, a direct search algorithm that does not use derivatives.

GSL , a C++ library which includes rootfinding routines.

LAWSON, a FORTRAN77 library which contains routines for solving least squares problems and singular value decompositions, by Lawson and Hanson.

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

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

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

SLATEC, 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, 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, a FORTRAN90 library which includes various zero finder routines.

Author:

Original FORTRAN77 version by Richard Brent; this FORTRAN77 version by John Burkardt.

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.sh, commands to compile the source code.

Examples and Tests:

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

List of Routines:

• GLOMIN seeks a global minimum of a function F(X) in an interval [A,B].
• LOCAL_MIN 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].
• ZERO_RC seeks the root of a function F(X) in an interval [A,B].