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 Post subject: How does Nonlinear solver know it has found local minimum?
PostPosted: Wed Aug 20, 2014 4:17 pm 
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Joined: Wed Aug 20, 2014 3:55 pm
Posts: 1
I'm using NLEQ to estimate a distortion model for a camera. I already have a Scilab code that estimates the distortion so I know a good solution and alglib's nonlinear solver NLEQ also finds the known solution but returns report code,
-4 ERROR: algorithm has converged to the
stationary point Xf which is local minimum of
f=F[0]^2+...+F[m-1]^2, but is not solution of
nonlinear system.

In this problem, the number of equations m=224 and the dimension of the state is n=61. How does NLEQ know that it has only found a local minimum and that there is a global minimum?


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 Post subject: Re: How does Nonlinear solver know it has found local minimu
PostPosted: Thu Aug 21, 2014 9:05 am 
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Joined: Fri May 07, 2010 7:06 am
Posts: 903
I think that you have too small EpsF (quantity which is set by NLEQSetCond function). If algorithm stops at point where |F|>EpsF, it considers this point at local extrema of F^2 which is NOT solution.

Try increasing EpsF... optimal value is problem-specific.


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