lsqcurvefit cost/optimization function

In the lsqcurvefit function, is there a way to change the output 'resnorm' to be a different cost or optimization function, such as the absolute value of the difference, or the log of that (instead of the square of the difference)?

Answer 1

[Star Strider]

The residual (the ‘raw’ difference between the fitted regression and the data) is the third output from lsqcurvefit. You can do whatever operations on it you want.

For example:

[x,resnorm,residual,exitflag,output] = lsqcurvefit(___);
abs_rsd = abs(residual);
log_abs_rsd = log(abs(residual));

[Steve bourke]

Thank you for your response, however what we want to know is if we can change the chi squared function it uses to optimize the fitting.

[Star Strider]

My pleasure.

Not to my knowledge.

If it’s not among the available options in the options structure, you can’t change it without hacking the code. I don’t recommend that even if it’s possible.

You can always write your own nonlinear curve-fitting routines. Having done that myself in FORTRAN back in the early 1980s, I don’t recommend it.

Answer 2

[John D'Errico]

No. There is no way to change the lsqcurvefit code to use a different measure of error. Ok, no way except for rewriting lsqcurvefit.

The point is, lsqcurvefit uses algorithms that are specific to a sum of SQUARES of residuals. lsqcurvefit is not a general optimizer, that you could somehow just tell it to use a different metric.

If that is your goal, you could in theory use a different tool, perhaps fminunc or some other totally general optimizer. Even that is subject to significant problems however. For example, a sum of absolute values would result in a non-differentiable objective function. That could result in a failure to converge for fminunc.

So IF you truly needed to use a different objective, then you would be best off using an optimizer that would not be subject to such a failure. That might mean fminsearch, or perhaps a genetic algorithm, or some other stochastic scheme like a particle swarm method.