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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">
<meta content="text/html; charset=ISO-8859-1"
http-equiv="Content-Type">
<meta name="GENERATOR" content="MSHTML 8.00.6001.18999">
<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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</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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