toms178, a Python code which uses the Hooke-Jeeves direct search algorithm to seek the minimizing point of a function F(X) of several variables, by Arthur Kaupe.

The Hooke_Jeeves algorithm does not required the function F(X) to be differentiable. It does not even require the function to be continuous, although it should probably only be "weakly discontinuous", like a step function, with finitely many well-separated jumps. In any case, the algorithm only examines function values, never derivatives, remembers the location of the best value encountered, and seeks to improve this value by a clever pattern search.

The user supplies a quantity rho, between 0 and 1, which controls how cautious or daring the search is, as well as a routine to evaluate the function, and a few input parameters.

A C version of the algorithm, as written by Mark Johnson, is available at

The text of many ACM TOMS algorithms is available online through ACM: or NETLIB:


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


toms178 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 code which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

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


Original Algol version by Arthur Kaupe; Python version by John Burkardt.


Source Code:

Last revised on 23 January 2016.