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<h3 class="section">1.15 A conjugate gradient method</h3>
<p><a name="index-cg_005fmin-21"></a>
<!-- cg_min ../inst/cg_min.m -->
<a name="XREFcg_005fmin"></a>
<div class="defun">
— Function File: [<var>x0</var>,<var>v</var>,<var>nev</var>] <b>cg_min</b> (<var> f,df,args,ctl </var>)<var><a name="index-cg_005fmin-22"></a></var><br>
<blockquote><p>NonLinear Conjugate Gradient method to minimize function <var>f</var>.
<h4 class="subheading">Arguments</h4>
<ul>
<li><var>f</var> : string : Name of function. Return a real value
<li><var>df</var> : string : Name of f's derivative. Returns a (R*C) x 1 vector
<li><var>args</var>: cell : Arguments passed to f.<br>
<li><var>ctl</var> : 5-vec : (Optional) Control variables, described below
</ul>
<h4 class="subheading">Returned values</h4>
<ul>
<li><var>x0</var> : matrix : Local minimum of f
<li><var>v</var> : real : Value of f in x0
<li><var>nev</var> : 1 x 2 : Number of evaluations of f and of df
</ul>
<h4 class="subheading">Control Variables</h4>
<ul>
<li><var>ctl</var>(1) : 1 or 2 : Select stopping criterion amongst :
<li><var>ctl</var>(1)==0 : Default value
<li><var>ctl</var>(1)==1 : Stopping criterion : Stop search when value doesn't
improve, as tested by ctl(2) > Deltaf/max(|f(x)|,1)
where Deltaf is the decrease in f observed in the last iteration
(each iteration consists R*C line searches).
<li><var>ctl</var>(1)==2 : Stopping criterion : Stop search when updates are small,
as tested by ctl(2) > max { dx(i)/max(|x(i)|,1) | i in 1..N }
where dx is the change in the x that occured in the last iteration.
<li><var>ctl</var>(2) : Threshold used in stopping tests. Default=10*eps
<li><var>ctl</var>(2)==0 : Default value
<li><var>ctl</var>(3) : Position of the minimized argument in args Default=1
<li><var>ctl</var>(3)==0 : Default value
<li><var>ctl</var>(4) : Maximum number of function evaluations Default=inf
<li><var>ctl</var>(4)==0 : Default value
<li><var>ctl</var>(5) : Type of optimization:
<li><var>ctl</var>(5)==1 : "Fletcher-Reves" method
<li><var>ctl</var>(5)==2 : "Polak-Ribiere" (Default)
<li><var>ctl</var>(5)==3 : "Hestenes-Stiefel" method
</ul>
<p><var>ctl</var> may have length smaller than 4. Default values will be used if ctl is
not passed or if nan values are given.
<h4 class="subheading">Example:</h4>
<p>function r=df( l ) b=[1;0;-1]; r = -( 2*l{1} - 2*b + rand(size(l{1}))); endfunction <br>
function r=ff( l ) b=[1;0;-1]; r = (l{1}-b)' * (l{1}-b); endfunction <br>
ll = { [10; 2; 3] }; <br>
ctl(5) = 3; <br>
[x0,v,nev]=cg_min( "ff", "df", ll, ctl ) <br>
<p>Comment: In general, BFGS method seems to be better performin in many cases but requires more computation per iteration
See also http://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient.
<p class="noindent"><strong>See also:</strong> <a href="XREFbfgsmin.html#XREFbfgsmin">bfgsmin</a>.
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