BRENT
Algorithms for Minimization Without Derivatives

BRENT, a C 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 FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

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

BISECTION_RC, a C 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 (RC).

brent_test

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

TEST_ZERO, a C library which implements test problems for the solution of a single nonlinear equation in one variable.

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

ZERO_RC, a C library which seeks solutions of a scalar nonlinear equation f(x) = 0, or a system of nonlinear equations, using reverse communication.

Author:

Original FORTRAN77 version by Richard Brent; C 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.c, the source code.
• brent.h, the include 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 round off unit.
• R8_MAX returns the maximum of two R8's.
• R8_SIGN returns the sign of an R8.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• 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].