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Your test case allowed me to a bug with respect to the management of
the output function in the case of Box's algorithm. I reported it at
:<br>
<br>
<a href="http://bugzilla.scilab.org/show_bug.cgi?id=8805">http://bugzilla.scilab.org/show_bug.cgi?id=8805</a><br>
<br>
Regards,<br>
<br>
Michaël<br>
<br>
Le 18/01/2011 09:19, Michaël Baudin a écrit :
<blockquote cite="mid:4D354D20.6050208@scilab.org" type="cite">
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Hi Paul,<br>
<br>
The status of the optimization is not good when the parameters are
left to the default values :<br>
<br>
-->neldermead_get(nm,"-status")<br>
ans =<br>
maxfuneval <br>
<br>
This means that the maximum number of function evaluations where
reached before the convergence was attained. All we need to do is
to increase the maximum number of function evaluations. In order
to get even closer to the optimum, we must also increase the
number of iterations.<br>
<br>
nm = neldermead_configure(nm,"-maxfunevals",200);<br>
nm = neldermead_configure(nm,"-maxiter",200);<br>
<br>
Once done, I get :<br>
<br>
-->xopt = neldermead_get(nm,"-xopt")<br>
xopt =<br>
1.0035954 <br>
1.0073491 <br>
<br>
This is quite a difficult case for Nelder-Mead's algorithm. The
simplex has to go through a long curved valley before reaching the
zone where the function begins to behave as a quadratic function.<br>
<br>
Rosenbrock's function has only one global minimum, at x=[1,1]. The
point x=[-1,1] is not a minimum.<br>
<br>
This is easy to check with Scilab. First, let us define the
function.<br>
<br>
function [f,G,H] = rosenbrock(x)<br>
f = 100*(x(2) - x(1)^2)^2 + (1 - x(1))^2;<br>
<br>
// Calculation of the gradient G vector<br>
G(1) = -400*x(1)*(x(2) - x(1)^2) - 2*(1 - x(1));<br>
G(2) = 200*(x(2) - x(1)^2);<br>
<br>
// Calculation of the Hessian matrix<br>
H(1,1) = -400*x(2) + 1200*x(1)^2 + 2;<br>
H(1,2) = -400*x(1);<br>
H(2,1) = -400*x(1);<br>
H(2,2) = 200;<br>
endfunction<br>
<br>
We get at x= [1,1] :<br>
<br>
-->[f,G,H] = rosenbrock([1,1])<br>
H =<br>
802. - 400. <br>
- 400. 200. <br>
G =<br>
0. <br>
0. <br>
f =<br>
0. <br>
<br>
This means that the gradient is zero, implying that the first
order conditions for unconstrained optimality are satisfied.
Moreover, the eigenvalues of the Hessian matrix are positive, as
shown below :<br>
<br>
-->spec(H)<br>
ans =<br>
0.3993608 <br>
1001.6006 <br>
<br>
This implies that the local curvature of the Rosenbrock function
is positive : x* is indeed a minimum.<br>
<br>
Now, at x=[-1,1], we get :<br>
<br>
-->[f,G,H] = rosenbrock([-1,1])<br>
H =<br>
802. 400. <br>
400. 200. <br>
G =<br>
- 4. <br>
0. <br>
f =<br>
4. <br>
<br>
The gradient is nonzero, which means that the first order
optimality conditions are not satisfied at x=[-1,1]. Rosenbrock's
function is a sum of squares.<br>
<br>
Best regards,<br>
<br>
Michaël<br>
<br>
<br>
Le 17/01/2011 11:18, Carrico, Paul a écrit :
<blockquote
cite="mid:55A12CBC06A8C9459DCE0BBEF8122FDC0498B09D@exchsrv.AUXITROL1"
type="cite">
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<div><font face="Arial" size="2"><span
class="307310710-17012011">Dear all</span></font></div>
<div><font face="Arial" size="2"><span
class="307310710-17012011"></span></font> </div>
<div><font face="Arial" size="2"><span
class="307310710-17012011">In the Rosenbrock equation it
is well known the 2 minima are (1,1) and (-1,1) ; in the
attached where I want to test several optimization macros
(and basic &particular functions) I've a different
result as descibed herebellow : is there a mistake in the
input file or does something go wrong ?</span></font></div>
<div><font face="Arial" size="2"><span
class="307310710-17012011"></span></font> </div>
<div><font face="Arial" size="2"><span
class="307310710-17012011">Please note the functions
inputs are as general as possible to be used with the
different macros (fminsearch, optim and so on)</span></font></div>
<div><font face="Arial" size="2"><span
class="307310710-17012011"></span></font> </div>
<div><font face="Arial" size="2"><span
class="307310710-17012011">Paul</span></font></div>
<div> </div>
<div> </div>
<div> </div>
<div><span class="307310710-17012011"><font face="Arial"
size="2">#################################################################"</font></span></div>
<div><span class="307310710-17012011"></span><font face="Arial"
size="2"><span style="font-size: 12pt;"><font size="2"> -
X1 optimized = 0.229978<br>
- X2 optimized = 0.0240434</font><br>
</span></font></div>
<div> </div>
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<br>
<br>
<pre class="moz-signature" cols="72">--
Michaël Baudin
Ingénieur de développement
<a moz-do-not-send="true" class="moz-txt-link-abbreviated" href="mailto:michael.baudin@scilab.org">michael.baudin@scilab.org</a>
-------------------------
Consortium Scilab - Digiteo
Domaine de Voluceau - Rocquencourt
B.P. 105 - 78153 Le Chesnay Cedex
Tel. : 01 39 63 56 87 - Fax : 01 39 63 55 94
</pre>
</blockquote>
<br>
<br>
<pre class="moz-signature" cols="72">--
Michaël Baudin
Ingénieur de développement
<a class="moz-txt-link-abbreviated" href="mailto:michael.baudin@scilab.org">michael.baudin@scilab.org</a>
-------------------------
Consortium Scilab - Digiteo
Domaine de Voluceau - Rocquencourt
B.P. 105 - 78153 Le Chesnay Cedex
Tel. : 01 39 63 56 87 - Fax : 01 39 63 55 94
</pre>
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