I have look around different ways to fit. So when do you know you have to use the cost function: sum((realdata-fittingdata).^2) or error = realdata-fittingdata? For example, for lsqnonlin, you would use 'error' to find do the optimization. However, for fminsearch or patternsearch, you would use the 'cost function.'
MATLAB: When to use cost function or error function for fitting
patternsearch
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