I'm currently studying the stopping criteria about fmincon using different algorithms and I'm wondering how are the tolerances are actually evaluated and compared in the built-in function fmincon. Especially I want to know what the units of the tolerances are compared to the objective function and variable. For instance, if the unit of the objective function or the cost is in dollars and the unit of the variables(X) is in km/h for every 30 mins, then what's the unit of the tolerances after the calculation. I already checked all these links: http://www.mathworks.com/help/optim/ug/tolerances-and-stopping-criteria.html and the webpages about fmincon and exit messages explanations.
The definition shown on the webpage still seem a little vague to me. For example, what type of norm did Matlab use in fmincon to compute |ceq(x)|, and what units does it return compare to the cost function and variables, km/h? (km/h)^2?. And I have same questions about |f(xi)-f(xi+1)| and TolFun. I was wondering if I can get any detailed mathematics formulation used for the calculation of the parameters and the tolerances related to the stopping criteria. For instance, in "fmincon" code and under interior point method, I found something such as if optimError
It would be great if I can get help with this.Appreciated!