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How to find the intersection between a polytope and a hyperplane

  1. Mar 22, 2013 #1
    Good afternoon!

    I am working on a problem, where I at some point have to find the intersection between a polytope and a hyperplan.

    Consider the following convex set:

    x2>=x1>=x4>=x3
    x1+x2+x3+x4=C1

    where C1 is a number. In matrixform it can be represented in the following way:

    A1*x<=b1,
    Aeq*x=beq

    where

    A1 =

    1 -1 0 0
    -1 0 0 1
    0 0 1 -1

    b1 =

    0
    0
    0

    Aeq= 1 1 1 1

    beq = C1


    I also have another set:
    x1+x4=C2
    x1+x2+x3+x4=C1

    I matrixform:
    Aeq2 * x = beq2

    Where

    Aeq2=

    1 0 0 1
    1 1 1 1

    beq2=

    C2
    C1



    My problem is that I need to find the intersection between these two sets, i.e. all the points where

    x2>=x1>=x4>=x3
    x1+x4=C2
    x1+x2+x3+x4=C1


    I used linear algebra a long time ago and have thus forgotten the most of it. Could you please tell me what I have to do or what I have to read to solve my problem. I will have to solve this problem in Matlab once I understand how to solve it.

    Thank you very much for your time and consideration!


    Alex
     
  2. jcsd
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