PRAXIS
Scalar Function Optimization

PRAXIS is a Python library which minimizes a scalar function of a vector argument, without needing derivative information, by Richard Brent.

PRAXIS seeks an M-dimensional point X which minimizes a given scalar function F(X). The code is a refinement of Powell's method of conjugate search directions. The user does not need to supply the partial derivatives of the function F(X). In fact, the function F(X) need not be smoothly differentiable.

Licensing:

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

Languages:

PRAXIS 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:

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.

Author:

Original FORTRAN77 version by Richard Brent. Python translation by John Burkardt.

Reference:

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

Source Code:

• beale.py, the Beale function.
• box.py, the Box function.
• chebyquad.py, the Chebyquad function.
• cube.py, the Cube function.
• helix.py, the Helix function.
• hilbert.py, the Hilbert function.
• powell3d.py, the Powell3d function.
• praxis.py, seeks an N-dimensional minimizer X of a scalar function F(X).
• r8_hypot.py, returns sqrt ( x^2 + y^2 ) as an R8;
• r8mat_print.py, prints an R8MAT;
• r8mat_print_some.py, prints some of an R8MAT;
• r8vec_print.py, prints an R8VEC;
• rosenbrock.py, the Rosenbrock function.
• singular.py, the Singular function.
• timestamp.py, prints the current YMDHMS date as a timestamp;
• tridiagonal.py, the Tridiagonal function.
• watson.py, the Watson function.
• wood.py, the Wood function.

Examples and Tests:

• praxis_test.py, calls all the tests.
• praxis_test.sh, runs all the tests.
• praxis_test.txt, the output file.

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