MATLAB: Non linear least squares problem using BFGS

bfgsnon linear inverse problem

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

Best Answer

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

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MATLAB: Fminunc: get Hessian approximation after each iteration

You could try running fminunc 1 iteration at a time in a for-loop and saving the 6th output arguments,


  options.MaxIter=1;
  for i=1:N
     
   [x,~,~,~,~,hessian{i}] = fminunc(fun,x,options);
  end

MATLAB: Gauss–Newton algorithm in Matlab

Simple answer: NO. There is no Gauss-Newton scheme in MATLAB. If you want it, you need to write it. If you want to solve the optimization problem in MATLAB, then use the optimization toolbox tools, or nlinfit, or the curve fitting toolbox. Or find Gauss-Newton code on the file exchange. (Generally, any code to implement Gauss-Newton that you will find on the file exchange is code written by novices, what I would consider poor code.)

Best Answer

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MATLAB: Fminunc: get Hessian approximation after each iteration

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