I am trying to learn how to model the KKT conditions of a simple economic dispatch problem. I have already run through my handwritten model and its KKT conditions, and the instructor confirmed they were correct. I am having issues with running my GAMS model, however, and this simply stems from lack of experience using it (hence why I am trying to learn).
The instructor I am working with is out of town and away from his email for around a week, but I still want to make some progress in what we're working on. Right now, as I said, I'm doing basic examples to get more familiar with the concepts and the GAMS code. I will include my code below. I wonder if my issue is how I am choosing to solve it; I did not know whether solving with nlp would be relevant since the complementary slackness conditions are nonlinear.
My actual model is below:
The set n represents the machines available to meet demand (which didn't factor into KKT conditions). Set t represents the hours over which the machines will operate (so machine n will operate from hours t = 1 to t = T).
C(n) is both the cost to operate machine n (in any hour) and the generalized gradient form of the objective function: (sum(t, sum(n, c(n)*x(n,t))).
Q(n) is the production capacity of generator n. It shows up in the generalized capacity constraint x(n,t) - Q(n) <= 0.
My instructor said that since I've declared all variables as strictly positive, I do not need the non-negativity constraints for x(n,t) and thus I do not need as many KKT conditions. However I wonder if setting mu(x,t) as a positive variable is causing issues. Does declaring a positive variable remove the chance it equals zero?
Any feedback would be appreciated. I am also trying to get used to using GAMS ability to manipulate similar algebraic structure with the KKT equation and the "sl" equations (which are the complementary slackness conditions).
Problems with syntax of GAMS
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