MATLAB: How can the least square optimizer LSQNONLIN be well conditiond

jacobileast squaresMATLABoptimization

Hi,
i am doing a least square optimasation with LSQNONLIN. The problem is that at a certain point I always get comlex values as result. This is coming from my logarithlc function. So my question is: is it possible to restrict the used parameters to positive values? my code looks sth like this:
options =  optimset('MaxIter',10000,'MaxFunEvals',50000,'FunValCheck','on','Algorithm',{'levenberg-marquardt',.005});
alfaZ = lsqnonlin(@myfun,fgalfa1,1e-7,1e-3,options);
function f = myfun(alfa)
global LR Stmp H;
f=Stmp(:)-log(LR*alfa(:))+H*alfa(:);
end
I already tried around with the options, but it didnt change anything yet. So the problem is that LSQNONLIN tries also negative values for alfa… If anybody has an idea how to overcome this problem, it would be great. Thanks for your help!

Best Answer

I suggest you use the lsqnonlin trust-region-reflective algorithm. As explained here, this algorithm satisfies bounds at every iteration.
It is also possible you should scale your problem so that your range of possible values is larger.
It appears that you have a 1-D problem (scalar alfa). If so, why not use fminbnd to minimize the sum of squares?
If your problem is not scalar, then you need to set vector values for your bounds. See Bound Constraints.
Alan Weiss
MATLAB mathematical toolbox documentation
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