Use R to Solve for Weights to Maximize a Variable

Consider a zoo object with N monthly rows, each of which has M columns; each column is a time series of momentum for a particular instrument. See attached file as an example. Create another zoo object that for each date, gives the weights for each of the M instruments that maximizes the weighted average momentum for that date. Constraints: 1) all weights for each date sum to 1 2) The total number of non-zero positions is X, where X<=M. That is, if I have 20 instruments, perhaps I want positions in only 5 of them where those 5 weights sum to 1.0 and the rest of the weights are zero. 3) There is a vector of maximum and minimum weights for each of the M instruments, which may all be the same (normal would be between 0 and 1) but which may differ, and may be negative. The winning bidder probably can do this in 10 minutes because he/she already has done optimizations of this type! I often have micro/mini projects like this because my R skills are fair, but it is just more efficient to get an expert to do it. You may use any optimization type you like: nloptr, DEopt, whatever.