how to regularized nonlinear least squares?

[Wei Guo]

  The energy has a fitting item and regularized item such as :

    || f(theta ) ||^2 + w || theta || ^2

   Where theta is a multi variable parameter.

    How to solve this problem using  ceres solver?

Thanks,

[Sameer Agarwal]

Wei,

Have you had a look at the ceres solver tutorial?

http://ceres-solver.org/nnls_tutorial.html

Sameer

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[Wei Guo]

 Yes, I read it. I don't know how to deal with the regularized item.  Do I treat it as a function F(x) = x? 

[Sameer Agarwal]

Yes. Or if you have a multiplier lambda in which case f(x)=sqrt(lambda)x.

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[hwdo...@gmail.com]

Should I weighting to the number of observations?  Suppose the number of observations is m,the number of theta is n.  I use w1 and w2 to weight the two terms. the formula is:

    w1/(2m) *sum_i(||f(xi,yi, theta||^2) + w2/n *||theta||^2  

 Where these {(xi,yi)} are observations. when m become larger, the result become bad. What's the problem? 

[Sameer Agarwal]

I am not sure I understand your question.

Sameer

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