<div dir="ltr"><div>Hi,</div>
<div> </div>
<div>note that your problem is very simple unconstrained optimization which is easy to solve just using a 2x2 matrix inversion!</div>
<div> </div>
<div>For a good reference on the topic read chapter 6 of this famous online book: <a href="http://www.stanford.edu/~boyd/cvxbook/">http://www.stanford.edu/~boyd/cvxbook/</a></div>
<div> </div>
<div>or simply read example 3 in chapter 8 of </div>
<div>Burden & Faires, Numerical analysis, 7ed. which is identical to your problem (I usually assign, like it, as a homework in undergraduate sci. comp. course).</div>
<div> </div>
<div>hope this helps</div>
<div> </div>
<div>RT</div>
<div> </div>
<div> </div>
<div class="gmail_quote">On Tue, Jun 15, 2010 at 1:23 AM, <span dir="ltr"><<a href="mailto:pierre-lin.pommier@fr.michelin.com">pierre-lin.pommier@fr.michelin.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid"><br><font face="sans-serif" size="2">Hello,</font> <br><br><font face="sans-serif" size="2">I'm looking for to solve an optimization problem. I have some experimental data and I want to minimize the difference (L2-norm) between the model and the measures.</font> <br>
<br><font face="sans-serif" size="2">I have some difficulties to link Ipopt solver : how can I take into account these experimental data in functions "eval_f", "eval_grad_f", "eval_g", "eval_jac_g" and "eval_h" ?</font> <br>
<br><font face="sans-serif" size="2">You gave an example to minimize a function without experimental data.</font> <br><br><font face="sans-serif" size="2">For instance, if my function is</font> <br><br><font face="sans-serif" size="2">y(p1, p2, x) = p1 * exp(p2 * x)</font> <br>
<br><font face="sans-serif" size="2">where p1 and p2 are my 2 parameters, x is my variable (the temperature for instance). So at each componant of x, called x_i, I must have a new point y(p1, p2, x_i)</font> <br><br><font face="sans-serif" size="2">the jacobian of my function is</font> <br>
<br><font face="sans-serif" size="2">exp(p2 * x)</font> <br><font face="sans-serif" size="2">p2 * p1 * exp(p2 * x)</font> <br><br><font face="sans-serif" size="2">for each x.</font> <br><br><font face="sans-serif" size="2">How can I program functions "eval_f", "eval_grad_f", "eval_g", "eval_jac_g" and "eval_h" ?</font> <br>
<br><font face="sans-serif" size="2">Thank you very much.</font> <br><br><font face="sans-serif" size="2">Sincerly,</font> <br><br><font face="sans-serif" size="2">Pierre-Lin Pommier</font> <br><font face="sans-serif" size="2">_______________________________________________________<br>
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<br></blockquote></div><br></div>