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<html>
<head>
<title>
TOMS178 - Minimization by Hooke-Jeeves Direct Search
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055" >
<h1 align = "center">
TOMS178 <br> Minimization by Hooke-Jeeves Direct Search
</h1>
<hr>
<p>
<b>TOMS178</b>
is a FORTRAN90 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.
</p>
<p>
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.
</p>
<p>
The user supplies a quantity <b>rho</b>, 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.
</p>
<p>
A C version of the algorithm, as written by Mark Johnson,
is available at
<a href = "http://www.netlib.org/opt/hooke.c">
http://www.netlib.org/opt/hooke.c</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TOMS178</b> is available in
<a href = "../../c_src/toms178/toms178.html">a C version</a> and
<a href = "../../cpp_src/toms178/toms178.html">a C++ version</a> and
<a href = "../../f77_src/toms178/toms178.html">a FORTRAN77 version</a> and
<a href = "../../f_src/toms178/toms178.html">a FORTRAN90 version</a> and
<a href = "../../m_src/toms178/toms178.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 = "../../f_src/compass_search/compass_search.html">
COMPASS_SEARCH</a>,
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>
<a href = "../../f_src/dqed/dqed.html">
DQED</a>,
a FORTRAN90 library which
solves constrained least squares problems.
</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 = "../../f_src/minpack/minpack.html">
MINPACK</a>,
a FORTRAN90 library which
solves systems of nonlinear equations, or the least squares minimization of the
residual of a set of linear or nonlinear equations.
</p>
<p>
<a href = "../../m_src/nelder_mead/nelder_mead.html">
NELDER_MEAD</a>,
a MATLAB program which
minimizes a scalar function of multiple variables using the Nelder-Mead algorithm.
</p>
<p>
<a href = "../../f_src/nl2sol/nl2sol.html">
NL2SOL</a>,
a FORTRAN90 library which
implements an adaptive nonlinear least-squares algorithm.
</p>
<p>
<a href = "../../f_src/praxis/praxis.html">
PRAXIS</a>,
a FORTRAN90 library which
minimizes a scalar function of several variables, without derivative information.
</p>
<p>
<a href = "../../f_src/test_nls/test_nls.html">
TEST_NLS</a>,
a FORTRAN90 library which
defines test problems
requiring the least squares minimization of a set of nonlinear functions.
</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/toms611/toms611.html">
TOMS611</a>,
a FORTRAN90 library which
optimizes a scalar functional of multiple variables.
</p>
<p>
<a href = "../../f77_src/uncmin/uncmin.html">
UNCMIN</a>,
a FORTRAN77 library which
can be used to seek the minimizer of a scalar functional
of multiple variables.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Original Algol version by Arthur Kaupe;
FORTRAN90 version by John Burkardt.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ul>
<li>
M Bell, Malcolm Pike,<br>
Remark on Algorithm 178: Direct Search,<br>
Communications of the ACM,<br>
Volume 9, Number 9, September 1966, page 684.
</li>
<li>
Robert Hooke, Terry Jeeves,<br>
Direct Search Solution of Numerical and Statistical Problems,<br>
Journal of the ACM,<br>
Volume 8, Number 2, April 1961, pages 212-229.
</li>
<li>
Arthur Kaupe,<br>
Algorithm 178:
Direct Search,<br>
Communications of the ACM,<br>
Volume 6, Number 6, June 1963, page 313.
</li>
<li>
FK Tomlin, LB Smith,<br>
Remark on Algorithm 178: Direct Search,<br>
Communications of the ACM,<br>
Volume 12, Number 11, November 1969, page 637-638.
</li>
</ul>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "toms178.f90">toms178.f90</a>, the source code;
</li>
<li>
<a href = "toms178.sh">toms178.sh</a>,
commands to compile the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "toms178_prb.f90">toms178_prb.f90</a>, the sample calling program;
</li>
<li>
<a href = "toms178_prb.sh">toms178_prb.sh</a>,
commands to compile, link and run the sample calling program.
</li>
<li>
<a href = "toms178_prb_output.txt">toms178_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BEST_NEARBY</b> looks for a better nearby point, one coordinate at a time.
</li>
<li>
<b>HOOKE</b> seeks a minimizer of a scalar function of several variables.
</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 = "../f90_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 12 February 2008.
</i>
<!-- John Burkardt -->
</body>
</html>