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Topic: can I form a linear contrained equations for this constraint?
Replies: 1   Last Post: Oct 4, 2012 8:26 AM

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Peter Spellucci

Posts: 221
Registered: 11/9/09
Re: can I form a linear contrained equations for this constraint?
Posted: Oct 4, 2012 8:26 AM
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MBALOVER <> writes:
>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.

your description of the problem must be highly incomplete:
your feasible domain consisting of the union of 3 lines through zero
is unbounded. a linear function on this domain will also be unbounded.
and, for example, one could ask why not to choose all points equal?
and one more remark: you cannot transform an ''or-condition'' in a
linear relation: otherwise the problem with milp would not exist.

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