# Minimization problem with integral constraint

2 views (last 30 days)
Esteban Garcia on 9 May 2022
Commented: Esteban Garcia on 11 May 2022
Hello, I'm working with a 2D numerical density profile. . I have a set of radius a maximum radius R and I want to find the best fit to the data r. I know that I can use maximum likelihood or another method, but I have problems with the constraints for , because I require that
At first I tried with bins and adjusted the curve with cftool, but I need more precision. So I want to use minimization with that constraint.
Thank you so much.

Matt J on 9 May 2022
Edited: Matt J on 9 May 2022
Perhaps you could reparametrize the curve as,
which automatically satisfies the constraint for any b and c. Moreoever, since this form has only two unknown parameters, it should be relatively easy to do a parameter sweep to find at least a good initial guess of b and c.
Esteban Garcia on 11 May 2022
Hello Matt it is much faster now without symbolyc and with log. Thank you
N=length(Rproj);
R=max(Rproj);
A=1000000
B=0
C=0
syms b c
for j=1:N
F(j)=log(2*Rproj(j)*(1+(Rproj(j)/b)^2)^c/(((b^2+R^2)^(c+1)-b^(2*c+2))/(b^(2*c)*(c+1))));
end
E=-sum(F);
fstr=string(E);
fstr=replace(fstr,'b','b(k)');
fstr=replace(fstr,'c','c(j)');
b=0.01:0.001:0.8
c=-1.405:0.001:-0.705
for k=1:length(b)
for j=1:length(c)
n=eval(fstr);
if n<A
A=n;
B=b(k);
C=c(j);
end
end
end

Mitch Lautigar on 9 May 2022
My suggestion is to use a smaller step size for <a,b,c> if you know what they are. Typically when you are trying to fix the curve, the only thing you can do is try to add in more datapoints. If you can provide some code, I can provide more feedback.

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