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<html>
<head>
<title>
FMINCON - Examples of Constrained Minimization using FMINCON
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FMINCON <br> Examples of Constrained Minimization using FMINCON
</h1>
<hr>
<p>
<b>FMINCON</b>
is a function included in MATLAB's Optimization Toolbox which
seeks the minimizer of a scalar function of multiple variables,
within a region specified by linear constraints and bounds.
</p>
<p>
A related function built into MATLAB is
<a href = "http://www.mathworks.com/help/techdoc/ref/fminsearch.html">
fminsearch</a>
which minimizes a scalar function of several variables using the
Nelder-Mead algorithm.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<i>x_opt</i> = fmincon ( <i>fun</i>, <i>x0</i>, <i>A</i>, <i>b</i>,
<i>Aeq</i>, <i>beq</i>, <i>lb</i>, <i>ub</i> )
</blockquote>
where
<ul>
<li>
<i>fun</i> is the "function handle"; that is, the name of an M-file
that defines the function, preceded by an "@" sign;
</li>
<li>
<i>x0</i> is an initial value for the optimizer;
</li>
<li>
<i>A, b</i> define a linear inequality constraint A * x <= b on the solution.
</li>
<li>
<i>Aeq, beq</i> define a linear equality constraint Aeq * x = beq on the solution.
</li>
<li>
<i>lb, ub</i> define bounds on the solution, lb <= x <= ub.
</li>
</ul>
</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>FMINCON</b> is available in
<a href = "../../m_src/fmincon/fmincon.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/asa047/asa047.html">
ASA047</a>,
a MATLAB library which
minimizes a scalar function of several variables using the Nelder-Mead algorithm.
</p>
<p>
<a href = "../../m_src/compass_search/compass_search.html">
COMPASS_SEARCH</a>,
a MATLAB 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 = "../../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,
by Jeff Borggaard.
</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 = "../../m_src/test_opt/test_opt.html">
TEST_OPT</a>,
a MATLAB library which
defines test problems
requiring the minimization of a scalar function of several variables.
</p>
<p>
<a href = "../../m_src/toms178/toms178.html">
TOMS178</a>,
a MATLAB library which
optimizes a scalar functional of multiple variables using the Hooke-Jeeves method.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Harald Niederreiter, Kevin McCurley,<br>
Optimization of functions by quasi-random search methods,<br>
Computing,<br>
Volume 22, Number 2, 1979, pages 119-123.
</li>
</ol>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "fmincon_test.m">fmincon_test.m</a>,
calls all the tests.
</li>
<li>
<a href = "fmincon_test_output.txt">fmincon_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "fmincon_test01.m">fmincon_test01.m</a>,
uses the Niederreiter-McCurley function #1.
</li>
<li>
<a href = "niederreiter_mccurley1.m">niederreiter_mccurley1.m</a>,
evaluates the Niederreiter-McCurley function #1.
</li>
<li>
<a href = "fmincon_test02.m">fmincon_test02.m</a>,
uses the Niederreiter-McCurley function #2.
</li>
<li>
<a href = "niederreiter_mccurley2.m">niederreiter_mccurley2.m</a>,
evaluates the Niederreiter-McCurley function #2.
</li>
<li>
<a href = "fmincon_test03.m">fmincon_test03.m</a>,
uses the Niederreiter-McCurley function #3.
</li>
<li>
<a href = "niederreiter_mccurley3.m">niederreiter_mccurley3.m</a>,
evaluates the Niederreiter-McCurley function #3.
</li>
<li>
<a href = "fmincon_test04.m">fmincon_test04.m</a>,
uses the Niederreiter-McCurley function #4.
</li>
<li>
<a href = "niederreiter_mccurley4.m">niederreiter_mccurley4.m</a>,
evaluates the Niederreiter-McCurley function #4.
</li>
<li>
<a href = "fmincon_test05.m">fmincon_test05.m</a>,
uses the Niederreiter-McCurley function #5.
</li>
<li>
<a href = "niederreiter_mccurley5.m">niederreiter_mccurley5.m</a>,
evaluates the Niederreiter-McCurley function #5.
</li>
<li>
<a href = "fmincon_test06.m">fmincon_test06.m</a>,
uses the Niederreiter-McCurley function #6.
</li>
<li>
<a href = "niederreiter_mccurley6.m">niederreiter_mccurley6.m</a>,
evaluates the Niederreiter-McCurley function #6.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 06 September 2010.
</i>
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