optimization of an objective function subjected to aggregated constraint

The objective function is as follows given in the images. The optimisation is to be done iteratively according to the inner loop but the constraint is according to the outer loop which is why i am unable to apply.

Answer 1

[Alan Weiss]

I suppose that the G_n are the control variables and that R_t are data. In that case it looks like a standard sort of linear programming problem. If the problem also has integer constraints as you hint, then it seems to be a MILP problem. See Problem-Based Optimization if you have a recent MATLAB version, or Solver-Based Optimization if you have an older version.

Alan Weiss

MATLAB mathematical toolbox documentation