In brief the problem can be stated as follows:

Given dependent variables Q_{i} i=1,...,N and independent variables x_{i, }y_{i}, and z_{i} i=1,...,N

which are related via the following system of N linear equations with parameters P_{1}, P_{2} and P_{3} :

Q_{i} = P_{1}x_{i}+P_{2}y_{i}+P_{3}z_{i} i=1,...,N

How to find the optimal values of P_{1}, P_{2} and P_{3} which satisfy the above system of linear equations subject to the following constraints:

P_{i}>=0 i=1,2,3

and P_{1}>=P_{2}P_{3}

Without the requirement of P_{1}>=P_{2}P_{3, }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.