# Solve Ax <= b with some unknown values of [b]? but with a relationship between them

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Ismaeel il 12 Dic 2016
Commentato: Matt J il 8 Ott 2017
I am using the solver "intlinprog" to solve an integer linear programming problem with inequality Ax<=b. This is one case I have already solved it. I have another case when some values of [b] vector are unknown, however, there is a relation between them and all u's are either 0 or 1.
Ex: . .
x1+x2+x3+x4+x5+x9 <= u1
x4+x6+x8 <= u2
. .
9 eq's with 9 unknown x's.
u1 and u2.. are unknown constant values but there is a relationship between them, say, u1+u2+u3+u4>3 (if we have 4 u's, one of them is zero and the rest are one).
I want the solver finds the values of u's (=0 or 1) in a way that it minimizes the total objective fn = min {x1+...+x2}. The result should be the values of x and u.
Can we solve such a problem?
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### Risposte (1)

Torsten il 12 Dic 2016
If the u's are also unknown, you will have to put them to the other unknowns x1,...,x9 as x10,x11,x12 and x13.
Best wishes
Torsten.
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Ismaeel il 12 Dic 2016
Modificato: Ismaeel il 12 Dic 2016
Thanks Torsten. I've already done your suggestion but that doesn't lead to a minimized solution. I've tested on 60x60 equations with 10 u's. The result of this data is known and equals to 14 x's instead of what I got which was 17 x's. This is after selecting only first x's that are not greater than the system size which is 60 from the whole result of x which includes u's but substracted.
Matt J il 8 Ott 2017
Torsten's suggestion should have worked. We would need to see code to analyze what went wrong.

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