<div style='font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10pt; color: #000000'><span style="color: rgb(0, 0, 0); font-family: 'Times New Roman'; font-size: medium; background-color: rgb(255, 255, 255); ">Michaël</span><span style="color: rgb(0, 0, 0); font-family: 'Times New Roman'; font-size: medium; background-color: rgb(255, 255, 255); "> ,</span><div style="color: rgb(0, 0, 0); "><br></div><div>I really appreciate your reply!! It helped me a lot.</div><div><br></div><div>Tkx!</div><div>Iwein<br><br><hr id="zwchr" style="color: rgb(0, 0, 0); font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10pt; "><div style="color: rgb(0, 0, 0); font-family: Helvetica, Arial, sans-serif; font-size: 12pt; font-weight: normal; font-style: normal; text-decoration: none; "><b>Van: </b>"michael.baudin [via Scilab / Xcos - Mailing Lists Archives]" <<a href="/user/SendEmail.jtp?type=node&node=4024684&i=0" target="_top" rel="nofollow" link="external">[hidden email]</a>><br><b>Aan: </b>"ivran" <<a href="/user/SendEmail.jtp?type=node&node=4024684&i=1" target="_top" rel="nofollow" link="external">[hidden email]</a>><br><b>Verzonden: </b>Dinsdag 7 augustus 2012 10:18:53<br><b>Onderwerp: </b>Re: constrained optimalisation with f(x,y) polynomals<br><br>

         Hi,

<br><br> There is no multivariate polynomial in Scilab, so you cannot

<br> create a 2-variable polynomial by adding to single-variable

<br> polynomials.

<br><br> With neldermead, it is relatively simple to find the minimum

of a 2-variable function, with nonlinear constraints.

<br> The script below prints the following output (in Scilab 5.3.3):

<br><br>  xopt

<br> 

<br>     10.239741

<br>     99.999999

<br> 

<br>  fopt

<br> 

<br>   - 870129.52

<br> 

<br>  copt

<br> 

<br>     1023.974

<br><br> This is not very accurate, but might be sufficient, depending

on your goals.

<br> If you need a more accurate computation, you may use the fmincon

<br> toolbox :

<br><br> <a href="http://atoms.scilab.org/toolboxes/fmincon" target="_blank" rel="nofollow" link="external">http://atoms.scilab.org/toolboxes/fmincon</a><br><br> or ipopt:

<br><br> <a href="http://atoms.scilab.org/toolboxes/sci_ipopt" target="_blank" rel="nofollow" link="external">http://atoms.scilab.org/toolboxes/sci_ipopt</a><br><br> But this might be more complicated, because these two tools

are still in alpha stage.

<br><br> Best regards,

<br><br> Michaël

<br><br> PS

<br><br> // Optimize an additive 2D polynomial with neldermead.

<br> function [f, c, index]=my2dpolynomial(x, index)

<br>     f = []

<br>     c = []

<br>     if ( index==2 | index==6 ) then

<br>         p1 = 1. - 2*x(1) + 3*x(1)^2 + 0.4*x(1)^3

<br>         p2 = 5. - 6*x(2) + 7*x(2)^2 + 0.8*x(2)^3

<br>         f = -p1 - p2

<br>     end

<br>     if ( index==5 | index==6 ) then

<br>         c1 = x(1) * x(2)

<br>         c2 = 1024 - c1

<br>         c = [c1 c2]

<br>     end

<br> endfunction

<br><br> rand("seed" , 0);

<br> x0 = [1. 1.].';

<br> // Compute f(x0)

<br> fx0 = my2dpolynomial ( x0 , 2 )

<br> // Compute the constraints:

<br> [ fx0 , cx0, index ] = my2dpolynomial ( x0 , 6 )

<br> // Setup optimization

<br> nm = neldermead_new ();

<br> nm = neldermead_configure(nm,"-numberofvariables",2);

<br> nm = neldermead_configure(nm,"-function",my2dpolynomial);

<br> nm = neldermead_configure(nm,"-x0",x0);

<br> nm = neldermead_configure(nm,"-method","box");

<br> nm = neldermead_configure(nm,"-nbineqconst",2);

<br> nm = neldermead_configure(nm,"-simplex0method","randbounds");

<br> nm = neldermead_configure(nm,"-boundsmin",[0.0 0.0]);

<br> nm = neldermead_configure(nm,"-boundsmax",[100.0 100.0]);

// Check that the cost function is correctly connected.

<br> [ nm , result ] = neldermead_function ( nm , x0 );

<br> //

<br> // Perform optimization

<br> nm = neldermead_search(nm);

<br> xopt = neldermead_get(nm,"-xopt");

<br> disp("xopt")

<br> disp(xopt)

<br> fopt = neldermead_get(nm,"-fopt")

<br> disp("fopt")

<br> disp(fopt)

<br> nm = neldermead_destroy(nm);

<br> disp("copt")

<br> disp(xopt(1)*xopt(2))

<br><br><br> On Mon, 6 Aug 2012 13:43:51 -0700 (PDT), ivran <<a target="_top" rel="nofollow" link="external">[hidden email]</a>>

<br> wrote:

<div class="shrinkable-quote"><div class='shrinkable-quote'><br>> hi guys,

<br>>

<br>> I'm having a big problem using scilab and some basic math. I would

<br>> really

<br>> appreciate some help with it 'cause i'm stuck - Consider the

<br>> following

<br>> problem:

<br>>

<br>> 2 polynomials, each describing a coordinate on its own. Together they

<br>> form a

<br>> 2D - f(x1,x2) surface which can have 2 - or more - maximums on a

<br>> certain

<br>> spot.

<br>>

<br>> f(x1) = p1 =                                         2             3

<br>>

<br>> 4             5             6

<br>>     55.044419 - 1.3570362x1 + 0.0162766x1 - 0.0001039x1 + 0.0000004x1

<br>> -

<br>> 4.592D-10x1 + 1.854D-13x1

<br>>

<br>> f(x2) = p2 =                        2             3             4

<br>> 5             6

<br>>     560.98702 - 23.76471x2 + 0.2962816x2 - 0.0009662x2 + 0.0000013x2

<br>> -

<br>> 8.576D-10x2 + 2.074D-13x2

<br>>

<br>> I have two problems here:

<br>>

<br>> 1) Does anyone know how to combine these 1D polynomials to a 2D

<br>> polynomial?

<br>> f(x1, x2) = px1x2 = p1 + p2

<br>> ...won't work. How can I solve this without overloading the '+'

<br>> method?

<br>>

<br>> 2) suppose I *could* combine these 2 functions:

<br>> f(x1, x2) = ...x1 + ...x2 + ...x1^n + ..x2^n

<br>> how can I find the maximum values of this function?, given the

<br>> following

<br>> constraints:

<br>> x1.x2 <= 1024

<br>> x1.x2 >= 0

<br>>

<br>> I'm (a little) familiar with Lagrange and the scilab procedures

<br>> regarding

<br>> this topic... but it would be very helpful if someone could post me a

<br>> example of this (or something close related) 2D constrained

<br>> optimization

<br>> problem.

<br>>

<br>> I'm really stuck at this... could you point me in the right

<br>> direction? ..tkx

<br>> in advance!!

<br>>

<br>> Iwein

<br>>

<br>>

<br>>

<br>>

<br>>

<br>>

<br>> --

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