Having problem with constrained minimization

You have a couple of problems. As Werner notes, one is that the eta function is implemented as a solve block, so that solve block has to be executed for every iteration of the minimize solve block. To make matters worse, you call the eta function inside summations in the Q function, and those are loops. You then call the Q function inside a summation, i.e. another loop, in the Err function. So you have an iterative solve block inside a loop, wihch is inside another loop, which is called by an iterative solve block. Fortunately, it is possible to rewrite the Q and Err functions to massively reduce the number of times the eta function has to be called.

Your other problem is that your problem looks like it's very badly conditioned. I think your objective function is very flat, so the solver wanders around a lot trying to find the minimum. This means a lot of iterations, but worse is that it makes it very sensitive to the guess values.

The attached worksheet converges to a solution in a reasonable time (although it's not fast!). To get a better solution you will have to play with the guess values and convergence tolerance though.