Local minima possible. lsqnonlin stopped because the size of the current step is less than the selected value of the step size tolerance.

I am using lsqnonlin solver for a non-linear data fitting problem.

I get a result which says "Local minima possible. lsqnonlin stopped because the size of the current step is less than the selected value of the step size tolerance".

I have a couple of questions on this regard.

1. After displaying the above warning, lsqnonlin gives a solution which is very close to my initial conditions to the parameter values. Why does this happen ?
2. What is the difference between local minima possible and local minima found while using these solvers ?
3. What should i change in optimoptions to find the local minima using lsqnonlin ?
4. How to calculate the standard error of parameter estimates using lsqnonlin ?

I have tried decreasing the function tolerance to 1E-10.

I have also tried decreasing the stepsize tolerance to 1E-10.

Neither of them worked.

What am i missing here ?

I kindly request you to help me in this regard.

Thanks and with best regards,

Prakash

Answer 1

[Alan Weiss]

Take a look at some suggestions in When the Solver Might Have Succeeded and When the Solver Succeeds.

Alan Weiss

MATLAB mathematical toolbox documentation

[Prakash Packirisamy]

Thanks a lot Alan Weiss for your recommendations.

I found it helpful.

I have one more follow up question along the same line.

1. How to determine the standard error of the parameter estimates using lsqnonlin

Thanks once again.

With regards,

Prakash

Answer 2

[Alan Weiss]

Perhaps this old example will be helpful. But maybe it is better to use nlparci from Statistics and Machine Learning Toolbox™.

Alan Weiss

MATLAB mathematical toolbox documentation