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lang=EN-GB>Hi Michaël,</SPAN><SPAN
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= o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p></SPAN></P>
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style="COLOR: black; mso-ansi-language: EN-GB" lang=EN-GB><FONT size=3><FONT
face="Times New Roman"> <o:p></o:p></FONT></FONT></SPAN></P>
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style="FONT-FAMILY: Arial; COLOR: blue; FONT-SIZE: 10pt; mso-ansi-language: EN-GB"
lang=EN-GB>Let me saying first (if necessary) I've good results using simplex
routines (either fminsearch <SPAN
class=239084709-26012011>macro </SPAN><SPAN class=239084709-26012011>or
</SPAN>Nelder-Mead one).</SPAN><SPAN
style="COLOR: black; mso-ansi-language: EN-GB" lang=EN-GB><o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="COLOR: black; mso-ansi-language: EN-GB" lang=EN-GB><FONT size=3><FONT
face="Times New Roman"> <o:p></o:p></FONT></FONT></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: blue; FONT-SIZE: 10pt; mso-ansi-language: EN-GB"
lang=EN-GB>It is well known (and mentioned in the literature for example) that
this algorithm is robust but slow ... but in some cases it's the last solution
(for not saying the last chance) !</SPAN><SPAN
style="COLOR: black; mso-ansi-language: EN-GB" lang=EN-GB><o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="COLOR: black; mso-ansi-language: EN-GB" lang=EN-GB><FONT size=3><FONT
face="Times New Roman"> <o:p></o:p></FONT></FONT></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="COLOR: black; mso-ansi-language: EN-GB" lang=EN-GB><FONT size=3><FONT
face="Times New Roman"> <o:p></o:p></FONT></FONT></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: blue; FONT-SIZE: 10pt; mso-ansi-language: EN-GB"
lang=EN-GB>Basically the purpose is to increase the convergence (and the
optimization total duration) ... especially when each FEA (= 1 loop) need more
than one hour !</SPAN><SPAN style="COLOR: black; mso-ansi-language: EN-GB"
lang=EN-GB><o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="COLOR: black; mso-ansi-language: EN-GB" lang=EN-GB><FONT size=3><FONT
face="Times New Roman"> <o:p></o:p></FONT></FONT></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: blue; FONT-SIZE: 10pt; mso-ansi-language: EN-GB"
lang=EN-GB>Commonly I noticed several decades (for not saying hundreds) of loop
with Nelder-Mead</SPAN><SPAN style="COLOR: black; mso-ansi-language: EN-GB"
lang=EN-GB><o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
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<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: blue; FONT-SIZE: 10pt">Paul</SPAN></P>
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style="FONT-FAMILY: Arial; COLOR: blue; FONT-SIZE: 10pt"></SPAN> </P>
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color=#000000></FONT></SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN> </P></FONT></SPAN>
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</DIV>
<DIV><FONT size=2 face=Tahoma><B>De :</B> Michaël Baudin
[mailto:michael.baudin@scilab.org] <BR><B>Envoyé :</B> mercredi 26 janvier
2011 08:13<BR><B>À :</B> users@lists.scilab.org<BR><B>Cc :</B>
Carrico, Paul<BR><B>Objet :</B> Re: [scilab-Users] Academic
question<BR></FONT><BR></DIV>
<DIV></DIV>Hi,<BR><BR>Indeed, the Nelder-Mead algorithm is rather slow, as can
be expected from an algorithm which does not rely on neither the gradient nor
the Hessian (or any approximation to it).<BR><BR>You can use the optim function
to solve your problem. In the optim help page :<BR><BR><A
href="http://www.scilab.org/product/man/optim.html">http://www.scilab.org/product/man/optim.html</A><BR><BR>search
for "Example: Optimizing with numerical derivatives".<BR><BR>The function does
not have to be analytic : the only thing that is required is that the function
can be evaluated.<BR><BR>Of course, the function should be smooth for the
function to work better. <BR> * If f and its gradient are continuous, optim
with the quasi-Newton and the limited BFGS algorithms should work well (i.e. try
the "qn" and "cg" options).<BR> * If f is discontinuous, only Nelder-Mead
can work (but is likely to have some problems to converge).<BR> * If f is
continous but its gradient is discontinous, you may try the "nd" option. It is a
special algorithms for functions in this class (e.g. min max_i f_i). Lemaréchal
is an expert on this topic.<BR><BR>Try it and you will see !<BR><BR>Best
regards,<BR><BR>Michaël<BR><BR><BR>Le 25/01/2011 12:38, Carrico, Paul a
écrit :
<BLOCKQUOTE cite=mid:55A12CBC06A8C9459DCE0BBEF8122FDC0498B0CC@exchsrv.AUXITROL1
type="cite">
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<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><FONT
size=3><FONT face="Times New
Roman">Dear
All,<O:P></O:P></FONT></FONT></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><O:P><FONT
size=3 face="Times New Roman"></FONT></O:P></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><FONT
size=3><FONT face="Times New
Roman">For some times
I’m testing Scilab macros for optimization purposes ; “optimization” has to be
intended here as an inverse method for fitting parameters (i.e. so that finite
element analysis fit test measurements).<O:P></O:P></FONT></FONT></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><O:P><FONT
size=3 face="Times New Roman"></FONT></O:P></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><FONT
size=3><FONT face="Times New
Roman">I tested basic
macros such as fminsearch for unbounded fitting as well as Nelder-Mead one for
bracketed parameters fitting. Basically the “cost function” is the normalized
Sum of the Square errors SSE from the FEA to the
measurements.<O:P></O:P></FONT></FONT></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><O:P><FONT
size=3 face="Times New Roman"></FONT></O:P></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><FONT
face="Times New Roman"><FONT size=3>In my FEA<SPAN
class=516203511-25012011>'s</SPAN> <SPAN class=516203511-25012011>the
</SPAN><SPAN class=516203511-25012011>variables </SPAN>can be material
parameters, spring stiffness’s, damping ratio and so on : the simplex method
is well adapted since the former <SPAN class=516203511-25012011>variables
</SPAN>are not analytically described in the cost function and since it’s not
necessary to calculate the gradient vector nor the Hessian matrix
…<O:P></O:P></FONT></FONT></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><O:P><FONT
size=3 face="Times New Roman"></FONT></O:P></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
lang=EN-GB><O:P></O:P></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><FONT
size=3><FONT face="Times New
Roman">If this method
is robust nevertheless it remains rather slow
!<O:P></O:P></FONT></FONT></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><O:P><FONT
size=3 face="Times New Roman"></FONT></O:P></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><O:P><FONT
size=3 face="Times New Roman"></FONT></O:P></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><FONT
size=3><FONT face="Times New
Roman">Is there a way
or another macro I can use to reduce the number of loops and the time
consuming consequently ?<O:P></O:P></FONT></FONT></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><O:P><FONT
size=3 face="Times New Roman"></FONT></O:P></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><FONT
face="Times New Roman"><FONT size=3><I><SPAN
lang=EN-GB><U>Nota</U></SPAN></I><SPAN lang=EN-GB> : I was thinking in OPTIM
macro but from my understanding the cost function need to be twice
differentiable at least <SPAN class=516203511-25012011> </SPAN>(for
the <SPAN class=516203511-25012011>G</SPAN>radient and the Hessian ) i.e.
analytically link to the parameters … isn’t it
?<O:P></O:P></SPAN></FONT></FONT></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><O:P><FONT
size=3 face="Times New Roman"></FONT></O:P></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><FONT
size=3><FONT face="Times New
Roman">Thanks in
advance for any advice (for a better
understanding)<O:P></O:P></FONT></FONT></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><O:P><FONT
size=3 face="Times New Roman"></FONT></O:P></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN lang=EN-GB><FONT
size=3><FONT
face="Times New
Roman">Paul<O:P></O:P></FONT></FONT></SPAN></P></FONT></DIV>
<DIV> </DIV><PRE>--------------------------------------------------------------------------------
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</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>
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