Optimization of multivariable function

Hi everybody!

I'm having some trouble trying to optimize a function. I want to minimize the function F defined as:

where Aexp is a vector containing experimental data and Asim is a vector of simulated data. The true problem comes when defining the simulation function:

So the optimization needs to be carried out changing a1, sigma and a2 values in order to make F minimum.

However I'm really stuck as I have been using symbolic functions but turns out the result is always 1. I don't know any other way to use integral fucntions, even if this one does not look like working.

Any ideas? Thanks!

[Milankumar Padhiyar]

can you show us how you defined the objective function using symbolic variables ?

[Blanca Castells]

right now I don't even have the optimization function, I'm trying to generate Asim array as:

sigma=5;
a1=1000000;
a2=126;
    
i1=iarray(1);

iarray=linspace(150,400,30);

asim=[];
for i=1:length(iarray)
    i2=iarray(i);
syms x y
fun1(x,y)=exp(-x/y);
int1=int(fun1,y,[i1,i2]);
fun2(x)= exp((-a1/5)*int1-(((x-a2)^2)/(2*sigma^2)));
int2=int(fun2,x,[0,Inf]);
coef=1/(sigma*(2*pi())^0.5);
Asim=coef*int2;
asim=[asim,double(vpa(Asim))];

end

[Blanca Castells]

I think that once I obtain Asim I could use lsqcurvefit to calculate F

[Walter Roberson]

With that sigma, a1, a2, then the results of Asim are not exactly 0, but they are smaller than 10^(-7000) so double() converts them to 0.

You can, by the way, rewrite:

sigma=5;
a1=1000000;
a2=126;

iarray=linspace(150,400,30);
i1=iarray(1);

syms x y I2
fun1(x,y)=exp(-x/y);
Int1 = int(fun1, y, [i1, I2]);
fun2 = exp((-a1/5)*Int1-(((x-a2)^2)/(2*sigma^2)));
Int2 = int(fun2, x, [0 inf]);
coef=1/(sigma*(2*pi())^0.5);
AAsim = coef*Int2;

aasim = subs(AAsim, I2, iarray);
asim = double(aasim);    %fails, values too small for MuPAD to work with

[Blanca Castells]

I have changed a1 and a2 values, but in order to obtain Asim stimations the values does not make "physical sense". However, thanks for the answer, I'll keep thinking about it and trying to figure out another way to code it :)