Solving a system of linear inequalities

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Cassandra Wong
Cassandra Wong 2016-7-27
评论： Edward Szymkowiak 2018-3-29
Dear all, I need your help to solve a system of linear inequalities. The system is as follows
Fx = [x1+x2; x1+x2+x3+x6+x7; x2+x3+x4+x6; x3+x4+x5+x7; x4+x5; x2+x3+x6; x2+x4+x7]
and Fx >= 1
given that x1,x2,...x7 can either = 0 or 1 (whole number)
How to solve x1,x2 up to x7 in MATLAB?
Thanks in advance.
Best Regards
Cassandra
  1 个评论
Torsten
Torsten 2016-7-27
Choose
x1 = x2 = x3 =...= x7 = 1
Then
Fx >= 1 (componentwise)
is satisfied.
Best wishes
Torsten.

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回答（1 个）

Bjorn Gustavsson
Bjorn Gustavsson 2016-7-27
编辑：John D'Errico 2016-7-27
...or if you want all points that satisfy the conditions you could do:
D = {[0 1],[0 1],[0 1],[0 1],[0 1],[0 1],[0 1]};
[X1,X2,X3,X4,X5,X6,X7] = ndgrid(D{:});
IOK = (X1+X2>=1 & X1+X2+X3+X6+X7>=1 & X2+X3+X4+X6>=1 & X3+X4+X5+X7>=1 & X4+X5>=1 & X2+X3+X6>=1& X2+X4+X7>=1);
HTH
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John D'Errico
John D'Errico 2016-7-27
编辑：John D'Errico 2016-7-27
The last [0 1] in your assignment of D was given as [01], with no space. So a pretty minor typo.
Edward Szymkowiak
Edward Szymkowiak 2018-3-29
I am having trouble decoding IOK. Here is a simpler version:
D = {[0 1 ],[0 1],[0 1 ] };
[X1,X2,X3] = ndgrid(D{:});
IOK = (X1+X2+X3>0 & -X1+X2-X3>0);
Every time I add another variable the dimension of IOK increases.
Is there some code to map IOK back into a readable form telling us what values of X(n) satisfy the system for n =1 to # of variables?
Thanks

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