In brief the problem can be stated as follows:
Given dependent variables Qi i=1,...,N and independent variables xi, yi, and zi i=1,...,N
which are related via the following system of N linear equations with parameters P1, P2 and P3 :
Qi = P1xi+P2yi+P3zi i=1,...,N
How to find the optimal values of P1, P2 and P3 which satisfy the above system of linear equations subject to the following constraints:
Without the requirement of P1>=P2P3, the problem can be solved with the Non-negative Least Squares Method of Lawson and Hanson. But with this additional constraint, I am stuck.
Your suggestions are welcome.