non linear least squares problem using BFGS

Hello,

I need to find solution to a non linear least squares problem using Gauss-Newton method, however I am only able to compute Jacobian matrix for a simple model, so I need to use updating methods like BFGS instead full Jacobian computation. Does anybody know how to solve this problem using Matlab?

Thanks

[Matt J]

That sounds like it could have doubtful convergence properties. Gauss-Newton is already not guaranteed to converge, even in its pure form with the exact Jacobian. Seems like using an approximate Jacobian might only make things worse. If Benji's answer doesn't work for you (because it's not Gauss-Newton), maybe you could elaborate on why Gauss-Newton is your only option.

[David Kusnirak]

Thanks for hint. As I'm trying to follow 'recipe' from an arcticle, I'd prefer the Gauss-Newton method. I've tried to write my own script, but it yields quite poor results, so I would like to compare it somehow with Matlab function to improve the results.

Answer 1

[Shashank Prasanna]

Do you want to code this yourself or is it OK to use something that comes with MATLAB?

For the FMINUNC function in the Optimization Toolbox, if set the Algorithm to Medium Scale it will use BFGS Quasi-Newton method with a cubic line search procedure.

Take a look at the following documentation page and scroll down to the section call Algorithm > Medium-Scale Optimization

http://www.mathworks.com/help/optim/ug/fminunc.html

[David Kusnirak]

Thank you. I'm going to try this way, but till now I didn't find out how to set the algorithm for the medium scale..

[Shashank Prasanna]

Do the following:

>> options = optimset('LargeScale','off');
>> x = fminunc(fun,x0,options)

I urge you to read the FMINUNC documentation:

http://www.mathworks.com/help/optim/ug/fminunc.html