BRENT
Algorithms for Minimization Without Derivatives

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

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.

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

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 FORTRAN90 library which minimizes a scalar function of several variables.

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

TEST_MIN, a MATLAB library which implements test problems for minimization of a scalar function of a scalar variable.

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

TEST_ZERO, a MATLAB library which defines some test functions for which zeroes can be sought.

TOMS178, a MATLAB 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; MATLAB 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:

• glomin.m, seeks a global minimum of a function F(X) in an interval [A,B].
• local_min.m, seeks a local minimum of a function F(X) in an interval [A,B].
• local_min_rc.m, seeks a local minimum of a function F(X) in an interval [A,B], using reverse communication.
• r8_epsilon.m, returns the R8 machine precision.
• r8_sign.m, returns the sign of an R8.
• timestamp.m, prints out the current YMDHMS date as a timestamp.
• zero.m, seeks the root of a function F(X) in an interval [A,B].
• zero_rc.m, seeks the root of a function F(X) in an interval [A,B] using reverse communication.

Examples and Tests:

• brent_test.m, a sample calling program.
• test_zero_all.m, tests ZERO on all the test functions.
• test_zero_rc_all.m, tests ZERO_RC on all the test functions.
• test_local_min_all.m, tests LOCAL_MIN on all the test functions.
• test_local_min_rc_all.m, tests LOCAL_MIN_RC on all the test functions.
• test_global_all.m, tests GLOMIN on all the test functions.
• test_zero_one.m, tests ZERO on one test function.
• test_zero_rc_one.m, tests ZERO_RC on one test function.
• test_local_min_one.m, tests LOCAL_MIN on one test function.
• test_local_min_rc_one.m, tests LOCAL_MIN_RC on one test function.
• test_global_one.m, tests GLOMIN on one test function.
• f_01.m, zero finder test function #1.
• f_02.m, zero finder test function #2.
• f_03.m, zero finder test function #3.
• f_04.m, zero finder test function #4.
• f_05.m, zero finder test function #5.
• g_01.m, local minimum test function #1.
• g_02.m, local minimum test function #2.
• g_03.m, local minimum test function #3.
• g_04.m, local minimum test function #4.
• g_05.m, local minimum test function #5.
• h_01.m, global minimum test function #1.
• h_02.m, globalminimum test function #2.
• h_03.m, global minimum test function #3.
• h_04.m, global minimum test function #4.
• h_05.m, global minimumr test function #5.
• brent_test_output.txt, the output file.

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