Trustworthy covariance matrix and standard deviation from lsqnonlin with 'Local minimum possible'

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Remus Mihail Prunescu 2014-11-5

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https://ww2.mathworks.cn/matlabcentral/answers/161394-trustworthy-covariance-matrix-and-standard-deviation-from-lsqnonlin-with-local-minimum-possible

评论： Minu Pilvankar 2019-10-21

I'm doing parameter estimation with lsqnonlin function and after many iterations I get ' Local minimum possible '. As an output I'm getting the covariance matrix and standard deviations too for my parameter set. My question is: even if I don't get the ' Local minimum found ' message, are the covariance matrix and standard deviations trustworthy? Their value are satisfactory to my case but are they are trustworthy with 'Local minimum possible' message?

I'm getting Local minimum possible due to the First-order optimality indicator, which is rather high (3.51 for my problem). It seems to be stuck at this value even if norm of step < 1e-10.

More details: I'm initializing lsqnonlin rather close to the optimal values because I'm using fminsearch to find a good initial value. fminsearch doesn't give the covariance matrix, so I'm using the result from fminsearch to initialize lsqnonlin and get the covariance matrix.