How run lsqcurvefit correctly?

Hi, I'm using lsqcurvefit to find values of sa , for different data input, in a nolinear function. Sometime lsqcurvefit give me correct results but sometime it gives strange results with this message:

Local minimum found. Optimization completed because the size of the gradient is less than the default value of the function tolerance. criteria details

this is the code that I use:

    fun1=@(sa,f1)(A.*g.^2./((2.*pi).^4.*f1.^5).*exp(-5./4.*(fp./f1).^4)).*gam.^exp(-0.5.*((f1-fp)./(sa.*fp)).^2);

options=optimset('MaxFunEvals',20000);
options=optimset('TolFun',10^-6);
options=optimset('MaxIter',10000);
options=optimset('TolX',10^-6);
li=0.001;
ls=0.2;

sa_new=lsqcurvefit(fun1,0.07,f1,S1,li,ls,options);

Where A,g,gam,fp are all parametres that I Know and f1 and S1 are the data that I have fit with function. Any suggest to find the correct values of sa? Thanks so much

Answer 1

[Alan Weiss]

Your variable sa seems to be a scalar taking values between 0.001 and 0.2. Have you plotted the sum of squares as a function of sa to see if there are multiple local optima?

FYI, that exit message states that lsqcurvefit has found a local solution. However, there is no guarantee that it found a global solution. Again, I recommend that you plot the function on your interval to see the local optima.

Most likely, the solution to your problem will be to start from a few other points in addition to the fixed 0.07 that you are using, and to take the best solution among the several local optima.

Alan Weiss

MATLAB mathematical toolbox documentation