TOMS178 is a Python library 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 http://www.netlib.org/opt/hooke.c
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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.
ASA047, a Python library which minimizes a scalar function of several variables using the Nelder-Mead algorithm.
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.
Original Algol version by Arthur Kaupe; Python version by John Burkardt.
You can go up one level to the Python source codes.