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<h3 class="section">20.2 Minimizers</h3>
<p><a name="index-local-minimum-2170"></a><a name="index-finding-minimums-2171"></a>
Often it is useful to find the minimum value of a function rather than just
the zeroes where it crosses the x-axis. <code>fminbnd</code> is designed for the
simpler, but very common, case of a univariate function where the interval
to search is bounded. For unbounded minimization of a function with
potentially many variables use <code>fminunc</code>. See <a href="Optimization.html#Optimization">Optimization</a>, for
minimization with the presence of constraint functions. Note that searches
can be made for maxima by simply inverting the objective function
(<code>Fto_max = -Fto_min</code>).
<!-- fminbnd scripts/optimization/fminbnd.m -->
<p><a name="doc_002dfminbnd"></a>
<div class="defun">
— Function File: [<var>x</var>, <var>fval</var>, <var>info</var>, <var>output</var>] = <b>fminbnd</b> (<var>fun, a, b, options</var>)<var><a name="index-fminbnd-2172"></a></var><br>
<blockquote><p>Find a minimum point of a univariate function. <var>fun</var> should be a
function
handle or name. <var>a</var>, <var>b</var> specify a starting interval. <var>options</var>
is a
structure specifying additional options. Currently, <code>fminbnd</code>
recognizes these options: <code>"FunValCheck"</code>, <code>"OutputFcn"</code>,
<code>"TolX"</code>, <code>"MaxIter"</code>, <code>"MaxFunEvals"</code>.
For description of these options, see <a href="doc_002doptimset.html#doc_002doptimset">optimset</a>.
<p>On exit, the function returns <var>x</var>, the approximate minimum point
and <var>fval</var>, the function value thereof.
<var>info</var> is an exit flag that can have these values:
<ul>
<li>1
The algorithm converged to a solution.
<li>0
Maximum number of iterations or function evaluations has been exhausted.
<li>-1
The algorithm has been terminated from user output function.
</ul>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002doptimset.html#doc_002doptimset">optimset</a>, <a href="doc_002dfzero.html#doc_002dfzero">fzero</a>, <a href="doc_002dfminunc.html#doc_002dfminunc">fminunc</a>.
</p></blockquote></div>
<!-- fminunc scripts/optimization/fminunc.m -->
<p><a name="doc_002dfminunc"></a>
<div class="defun">
— Function File: <b>fminunc</b> (<var>fcn, x0</var>)<var><a name="index-fminunc-2173"></a></var><br>
— Function File: <b>fminunc</b> (<var>fcn, x0, options</var>)<var><a name="index-fminunc-2174"></a></var><br>
— Function File: [<var>x</var>, <var>fvec</var>, <var>info</var>, <var>output</var>, <var>grad</var>, <var>hess</var>] = <b>fminunc</b> (<var>fcn, <small class="dots">...</small></var>)<var><a name="index-fminunc-2175"></a></var><br>
<blockquote><p>Solve an unconstrained optimization problem defined by the function
<var>fcn</var>.
<var>fcn</var> should accepts a vector (array) defining the unknown variables,
and return the objective function value, optionally with gradient.
In other words, this function attempts to determine a vector <var>x</var> such
that <var>fcn</var><code> (</code><var>x</var><code>)</code> is a local minimum.
<var>x0</var> determines a starting guess. The shape of <var>x0</var> is preserved
in all calls to <var>fcn</var>, but otherwise is treated as a column vector.
<var>options</var> is a structure specifying additional options.
Currently, <code>fminunc</code> recognizes these options:
<code>"FunValCheck"</code>, <code>"OutputFcn"</code>, <code>"TolX"</code>,
<code>"TolFun"</code>, <code>"MaxIter"</code>, <code>"MaxFunEvals"</code>,
<code>"GradObj"</code>, <code>"FinDiffType"</code>,
<code>"TypicalX"</code>, <code>"AutoScaling"</code>.
<p>If <code>"GradObj"</code> is <code>"on"</code>, it specifies that <var>fcn</var>,
called with 2 output arguments, also returns the Jacobian matrix
of right-hand sides at the requested point. <code>"TolX"</code> specifies
the termination tolerance in the unknown variables, while
<code>"TolFun"</code> is a tolerance for equations. Default is <code>1e-7</code>
for both <code>"TolX"</code> and <code>"TolFun"</code>.
<p>For description of the other options, see <code>optimset</code>.
<p>On return, <var>fval</var> contains the value of the function <var>fcn</var>
evaluated at <var>x</var>, and <var>info</var> may be one of the following values:
<dl>
<dt>1<dd>Converged to a solution point. Relative gradient error is less than
specified
by TolFun.
<br><dt>2<dd>Last relative step size was less that TolX.
<br><dt>3<dd>Last relative decrease in function value was less than TolF.
<br><dt>0<dd>Iteration limit exceeded.
<br><dt>-3<dd>The trust region radius became excessively small.
</dl>
<p>Optionally, fminunc can also yield a structure with convergence statistics
(<var>output</var>), the output gradient (<var>grad</var>) and approximate Hessian
(<var>hess</var>).
<p>Note: If you only have a single nonlinear equation of one variable, using
<code>fminbnd</code> is usually a much better idea.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dfminbnd.html#doc_002dfminbnd">fminbnd</a>, <a href="doc_002doptimset.html#doc_002doptimset">optimset</a>.
</p></blockquote></div>
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