If I have data series and a set of constraints and want to predict the most likely values, what is the right algorithm or approach? For example, given the data table as follows:
The first three rows illustrate typical data values. Imagine we have dozens or hundreds of such rows. The constraints on the system are as follows:
G1 + G2 + G3 + G4 == D1 + D2 + D3
G1 + G2 = D1 - C1
G3 = D2 + C1 - C2
G4 = D3 + C2
So, given D1, D2 and D3 we need to predict G1, G2, G3, G4, C1, and C2. Note that there may not necessarily be enough information to solve the system by linear programming alone and so some kind of trend analysis or probability distribution might need to be made.
What is the right algorithm or approach to solve a problem like this?