constrained parameter fitting using fmincon

sandrala

2012 12 11

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8 次查看（30 天）

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Hi,

I want to do a parameter optimization. So far I was using lsqcurvefit to fit observed data with a function of the following form:

function [F] = datamatch(p,xdata,non0Indices,v1,v2,D,p0,q,g,lnc)

   x2=p(1);
   x3=p(2);
   x1=p(3:lnc+2);
   X1=zeros(size(xdata(:,1)));
   X1(non0Indices) = x1;
   p = x2 - x3 * log(xdata/q)
   F = (x1*v1) + (D * (1-(1-p/p0)^g) / (v2(1-p/p0)^g) )

whereby v1, v2, D, p0, g, q are scalar factors, x1, x2, x3 are the fitting parameters, x2 and x3 are scalars while x1 can have different values at a part of the dataset and is 0 everywhere else.

Unfortunately lsqcurvefit does not allow to set constraints, so my x1, x2, x3 become complex (which I do not want). I think I have to reformulate my problem to a least squares minimization using fmincon.

my constraints should be: x2>0 x2 - x3 * log(r/q) < 2p0

in order to avoid complex fitting parameters as an output.

My question is - how do I have to rewrite my function so that fmincon would work and deliver the optimal parameters x1, x2, x3 so that the term d - F(m)^2 will be at its minimum? The help for fmincon is abit cryptic to me. Where can I put in my observables, model function(F see above), initial optimization parameters?