What is lambda in lsqcurvefit?

lsqcurvefit returns the lambda values as a structure with fields lower and upper. But according to the Levenberg-Marquardt algorithm

,

where we have to specify the initial value of lambda, which is a scalar and it changes its value after each iteration.

Why is the lambda returned by the lsqcurvefit function having two vectors for upper and lower separately and why are they zeros in most of the cases?

Answer 1

[Matt J]

The lambda returned by lsqcurvefit are not Levenberg-Marquardt parameters. They are the Lagrange multiplers at the solution. If the Lagrange multipliers are zero most of the time, it is probably because your solutions tend not to lie at the upper and lower boundaries.

[Prashant Govindarajan]

So is there any way to obtain the parameter λ (damping parameter) from the lsqcurvefit function? I require it to calculate the standard errors of the estimated parameters.

[Matt J]

You can use the OutputFcn option to get it, or display it to the screen (to some precision) by settings the Display option to 'iter', as described here,

https://www.mathworks.com/help/optim/ug/output-function.html#f11028