Find intersection between two sets

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

[Titus Edelhofer]

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

[Aleksandrs]

Hi Titus,

Any representation would be great. I didn't write anything in the text, because I thought maybe some experts will get an idea that I don't have when they read my post or maybe Maybe matlab has a built in function or something.

But personally I thought finding all the extreme points. Then I can check whether everything between two given points is included in the intersection of these two sets.

Thank you!