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Re: can I form a linear contrained equations for this constraint?
Posted:
Oct 4, 2012 8:26 AM


MBALOVER <mbalover9@gmail.com> 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 ''orcondition'' in a linear relation: otherwise the problem with milp would not exist. hth peter



