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Question: Linear Optimization with nonlinear inequality constraints

Question:Linear Optimization with nonlinear inequality constraints

tlee 10 Maple
inequal
December 16 2014
2

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:

Pi>=0   i=1,2,3

and  P1>=P2P3

 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.

 

 

 

 
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