I basically just want to know if it is possible to find a closed form solution to the following situation...
I want to find the maximum of two summations added together. The catch is, I want to maximize with respect to the limits of the summation- which is in the function as well (I am summing over time, hence I want to find the time which maximizes the expression). AND I want the upper limit of one summation and the lower limit on the next summation to be the value time value that I found. So in short, I am summing over t, I want to optimize with respect to t, and I want to sum to t* on the first and from t* to infinity on the next.
Any help, even if its just a suggestion of where to look, would be warmly appreciated,