compass_search, a Fortran90 code which seeks the minimizer of a scalar function of several variables using compass search, a direct search algorithm that does not use derivatives.

The algorithm, which goes back to Fermi and Metropolis, is easy to describe. The algorithm begins with a starting point X, and a step size DELTA.

For each dimension I, the algorithm considers perturbing X(I) by adding or subtracting DELTA.

If a perturbation is found which decreases the function, this becomes the new X. Otherwise DELTA is halved.

The iteration halts when DELTA reaches a minimal value.

The algorithm is not guaranteed to find a global minimum. It can, for instance, easily be attracted to a local minimum. Moreover, the algorithm can diverge if, for instance, the function decreases as the argument goes to infinity.


The information on this web page is distributed under the MIT license.


compass_search is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:


asa047, a Fortran90 code which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

praxis, a Fortran90 code which implements the principal axis method of Richard Brent for minimization of a function without the use of derivatives.

test_opt, a Fortran90 code which defines test problems requiring the minimization of a scalar function of several variables.

test_opt_con, a Fortran90 code which defines test problems for the minimization of a scalar function of several variables, with the search constrained to lie within a specified hyper-rectangle.

toms178, a Fortran90 code which optimizes a scalar functional of multiple variables using the Hooke-Jeeves method.


John Burkardt


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Source Code:

Last revised on 11 June 2020.