Find intersection between two sets
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Hello,
I would be very grateful if you could help me with the following problem.
Consider a convex set represented by:
Ax<=b and x1+x2+x3+x4=22.0853
where
A =
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
1 1 0 0
1 0 1 0
1 0 0 1
0 1 1 0
0 1 0 1
0 0 1 1
1 1 1 0
1 1 0 1
1 0 1 1
0 1 1 1
and
b =
5.8737
20.5204
22.7264
7.7624
17.1473
26.6984
5.8084
21.2802
25.4698
20.2316
21.8626
21.4442
23.6201
22.8401
So, this convex set consists of all points that sum up to 22.0853 and that satisfy Ax<=b.
Next, I have another set: x2>=x1>=x4>=x3
In matrixform it can be represented in the following way:
A1x<=b1, where
A1 =
1 -1 0 0
-1 0 0 1
0 0 1 -1
b1 =
0
0
0
I know that the following point is in the intersection of these two sets (found by quadprog):
x1=
2.9042
13.3727
2.9042
2.9042
My problem is that I want to find not only one, but the whole set of points, which are in both above mentioned sets (the intersection between these sets). Is it possible to solve this problem in Matlab?
Thank you very much for your time and consideration!
Alex
2 Comments
Titus Edelhofer
on 18 Mar 2013
Hi Alex,
hmm, how do you think should this look like? If it's not a single point it will be an area (of infinite number of points then).
Titus
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