Date: Oct 3, 2012 6:28 PM
Subject: can I form a linear contrained equations for this constraint?

Dear all,

In my optimization problem, the independent variables are ten points in 2D space: ( x1, y1), (x2, y2), ..., (x10, y10). The constraint is that these ten points should lie on either one of 3 lines with known equations:

y = a1* x;
y = a2* x;
y = a3* x;

For now, I can form a non linear constraint as

(y1 - a1*x1)* (y1 - a2*x1) * (y1 - a3*x1) = 0
(y2 - a1*x2)* (y2 - a2*x2) * (y2 - a3*x2) = 0
(y10 - a1*x10)* (y10 - a2*x10) * (y10 - a3*x10) = 0

However I wonder if it is possible to form it in a form of a linear constraint so that I can use my linear programming code to solve the problem ( the cost function is already linear to the independent variables). Do you have any idea to do it?

Or if not, can you have any idea to rewrite the constraint in a simplifier form?

Thank you.