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<html>
<head>
<title>
COMPASS_SEARCH - The Compass Search Optimization Algorithm
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
COMPASS_SEARCH <br> The Compass Search Optimization Algorithm
</h1>
<hr>
<p>
<b>COMPASS_SEARCH</b>
is a FORTRAN90 library which
seeks the minimizer of a scalar function of several variables
using compass search, a direct search algorithm that does not use derivatives.
</p>
<p>
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.
</p>
<p>
For each dimension I, the algorithm considers perturbing X(I) by adding
or subtracting DELTA.
</p>
<p>
If a perturbation is found which decreases the function, this becomes the
new X. Otherwise DELTA is halved.
</p>
<p>
The iteration halts when DELTA reaches a minimal value.
</p>
<p>
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.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>COMPASS_SEARCH</b> is available in
<a href = "../../c_src/compass_search/compass_search.html">a C version</a> and
<a href = "../../cpp_src/compass_search/compass_search.html">a C++ version</a> and
<a href = "../../f77_src/compass_search/compass_search.html">a FORTRAN77 version</a> and
<a href = "../../f_src/compass_search/compass_search.html">a FORTRAN90 version</a> and
<a href = "../../m_src/compass_search/compass_search.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/asa047/asa047.html">
ASA047</a>,
a FORTRAN90 library which
minimizes a scalar function of several variables using the Nelder-Mead algorithm.
</p>
<p>
<a href = "../../m_src/entrust/entrust.html">
ENTRUST</a>,
a MATLAB program which
minimizes a scalar function of several variables using trust-region methods.
</p>
<p>
<a href = "../../m_src/nelder_mead/nelder_mead.html">
NELDER_MEAD</a>,
a MATLAB program which
minimizes a scalar function of several variables using the Nelder-Mead algorithm.
</p>
<p>
<a href = "../../f_src/praxis/praxis.html">
PRAXIS</a>,
a FORTRAN90 library which
implements the principal axis method of Richard Brent for minimization of
a function without the use of derivatives.
</p>
<p>
<a href = "../../f_src/test_opt/test_opt.html">
TEST_OPT</a>,
a FORTRAN90 library which
defines test problems
requiring the minimization of a scalar function of several variables.
</p>
<p>
<a href = "../../f_src/test_opt_con/test_opt_con.html">
TEST_OPT_CON</a>,
a FORTRAN90 library 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.
</p>
<p>
<a href = "../../f_src/toms178/toms178.html">
TOMS178</a>,
a FORTRAN90 library which
optimizes a scalar functional of multiple variables using the Hooke-Jeeves method.
</p>
<h3 align = "center">
Author:
</h3>
<p>
John Burkardt
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Evelyn Beale,<br>
On an Iterative Method for Finding a Local Minimum of a Function
of More than One Variable,<br>
Technical Report 25, <br>
Statistical Techniques Research Group,<br>
Princeton University, 1958.
</li>
<li>
Richard Brent,<br>
Algorithms for Minimization without Derivatives,<br>
Dover, 2002,<br>
ISBN: 0-486-41998-3,<br>
LC: QA402.5.B74.
</li>
<li>
Charles Broyden,<br>
A class of methods for solving nonlinear simultaneous equations,<br>
Mathematics of Computation,<br>
Volume 19, 1965, pages 577-593.
</li>
<li>
David Himmelblau,<br>
Applied Nonlinear Programming,<br>
McGraw Hill, 1972,<br>
ISBN13: 978-0070289215,<br>
LC: T57.8.H55.
</li>
<li>
Tamara Kolda, Robert Michael Lewis, Virginia Torczon,<br>
Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods,<br>
SIAM Review,<br>
Volume 45, Number 3, 2003, pages 385-482.
</li>
<li>
Ken McKinnon,<br>
Convergence of the Nelder-Mead simplex method to a nonstationary point,<br>
SIAM Journal on Optimization,<br>
Volume 9, Number 1, 1998, pages 148-158.
</li>
<li>
Zbigniew Michalewicz,<br>
Genetic Algorithms + Data Structures = Evolution Programs,<br>
Third Edition,<br>
Springer, 1996,<br>
ISBN: 3-540-60676-9,<br>
LC: QA76.618.M53.
</li>
<li>
Jorge More, Burton Garbow, Kenneth Hillstrom,<br>
Testing unconstrained optimization software,<br>
ACM Transactions on Mathematical Software,<br>
Volume 7, Number 1, March 1981, pages 17-41.
</li>
<li>
Michael Powell,<br>
An Iterative Method for Finding Stationary Values of a Function
of Several Variables,<br>
Computer Journal,<br>
Volume 5, 1962, pages 147-151.
</li>
<li>
Howard Rosenbrock,<br>
An Automatic Method for Finding the Greatest or Least Value of a Function,<br>
Computer Journal,<br>
Volume 3, 1960, pages 175-184.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "compass_search.f90">compass_search.f90</a>, the source code.
</li>
<li>
<a href = "compass_search.sh">compass_search.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "compass_search_prb.f90">compass_search_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "compass_search_prb.sh">compass_search_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "compass_search_prb_output.txt">compass_search_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>COMPASS_SEARCH</b> carries out a direct search minimization algorithm.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 05 January 2012.
</i>
<!-- John Burkardt -->
</body>
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</html>