Wow. I'll have to think about this. If I make any progress, I'll post an answer. BTW, here we have n=2. Is that reasonable value of n, or are you dealing with much larger values too? I'm assuming an algorithmic solution, if I can find one, is acceptable, and I'd like to have an idea of the dimension.

n_i should ideally be small. Maximum around 10-20. You can assume that n_i <= N if you want, for some given N. I will be more than happy to see an iterative solution (assuming it is not brute force because that will not work for large i)

Yes, I'm not thinking of brute force. May I ask in what connection this problem arises, if it's not too complicated, and not confidential?

This equation is coming up there. I am trying to make some optimizations. If I can solve this equation, it will help me there.

Interesting. As I said, I'll have to think about this, and if I come up with anything, I'll let you know. Goodbye.

Thanks. Goodbye to you too.