BRENT
Algorithms for Minimization Without Derivatives

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

BISECTION_RC, a Python 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).

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

LOCAL_MIN_RC, a Python library which finds a local minimum of a scalar function of a scalar variable, without the use of derivative information, using reverse communication (RC), by Richard Brent.

PRAXIS, a Python library which minimizes a scalar function of several variables, without requiring derivative information, by Richard Brent.

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

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

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

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.py, seeks a global minimum of a function F(X) in an interval [A,B].
• local_min.py, seeks a local minimum of a function F(X) in an interval [A,B].
• local_min_rc.py, seeks a local minimum of a function F(X) in an interval [A,B], using reverse communication.
• zero.py, seeks the root of a function F(X) in an interval [A,B].
• zero_rc.py, seeks the root of a function F(X) in an interval [A,B] using reverse communication.

Examples and Tests:

• brent.py, a sample calling program.
• brent.sh, calls all the tests.
• brent.txt, the output file.

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