The Compass Search Optimization Algorithm

COMPASS_SEARCH is a C library 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 computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


COMPASS_SEARCH 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.

Related Data and Programs:

ASA047, a C library which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

ENTRUST, a MATLAB program which minimizes a scalar function of several variables using trust-region methods.

NELDER_MEAD, a MATLAB program which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

PRAXIS, a FORTRAN90 library which implements the principal axis method of Richard Brent for minimization of a function without the use of derivatives.

TEST_OPT, a C++ library which defines test problems requiring the minimization of a scalar function of several variables.

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


John Burkardt


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    Technical Report 25,
    Statistical Techniques Research Group,
    Princeton University, 1958.
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    Algorithms for Minimization without Derivatives,
    Dover, 2002,
    ISBN: 0-486-41998-3,
    LC: QA402.5.B74.
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    Mathematics of Computation,
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    SIAM Review,
    Volume 45, Number 3, 2003, pages 385-482.
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    Volume 9, Number 1, 1998, pages 148-158.
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    Volume 3, 1960, pages 175-184.

Source Code:

Examples and Tests:

List of Routines:

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

Last revised on 14 January 2012.