lsqcurvefit answer upon termination?

I'm curious about what answer lsqcurvefit is giving me when it terminates. When the program ends due to reaching number of iterations, does the answer (x) come from the last iteration or does it return the best answer based on previous iterations? By best I mean lowest first order optimality measure, step size, function tolerance size, etc.

[Torsten]

x and fval come from the last iteration.

[Nicholas Ross]

@Torsten thanks for the response. Is there a way to change it to where it sets x and fval based on the lowest output of either first order optimality, step size, or function tolerance? For example if the 45th iteration showed the lowest stepsize, use the values at that iteration to set x

Answer 1

[Matt J]

You can use a nested OutputFcn, like in this example,

https://www.mathworks.com/help/matlab/math/output-functions.html#bsgpq6q-31

to save the entire iteration history of x and resnorm values. You can then retrospectively pick the solution that you want from the whole iteration sequence.

You could also modify this example to save only the best-so-far x vector, rather than the whole history.

[Nicholas Ross]

Thanks @Matt J. I'm playing around with this now to see if I can get this to work. Regarding the output, there's 'f(x)', norm of step, first-order optimality, etc. My understanding is that 'f(x)' is the model prediction, 'norm of step' is the current step size at that iteration, and 'first order optimality' tells you if you're heading in the right direction at that iteration. Which is the better metric to look at when determining which is the best stopping point (when f(x), step size, function tolerancee, or optimality is smallest)? Or does each iteration have the best guess each time?

[Torsten]

The "best" iteration is of course the one where f(x) is minimum (assuming possible constraints on x are satisfied).

[Nicholas Ross]

Thanks for clarifying this. It seems obvious enough but being new to this area I wasn't quite sure if I was missing something.

[Torsten]

The variable "resnorm" in the output from "lsqcurvefit" represents f(x).

[Nicholas Ross]

@Torsten thanks for this note. That actually cleared up another question I had.