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Homework Help: Duality theory

  1. Oct 11, 2005 #1
    Obtain an upper bound for the optimal value in the following problem;
    Max (4x_1 + x_2 + 2x_3 + 3x_4 )
    2x_1 - x_2 + x_3 - 2x_4 <= 2
    7x_1 + x_2 + 5x_3 + 10x_4 <= 4
    2x_1 + 3x_2 - x_3 - x_4 <= 2
    x_i >= 0 , i= 1,2,3,4

    any hint.help. please.

    note: >= means > or equal to
    <= means < or equal to


    I understnad how to find the optimal value...but how do i find the
    upper bound?
    i dont really understand what is meant by the Upper Bound??

  2. jcsd
  3. Oct 13, 2005 #2
    Definition of upper bound:

    Given an ordered set [tex] X and A \subset X , s \in X is its "upper bound" ( sup\{A\}) \leftrightharpoons \forall x \in A, x \preceq s et \forall y \prec s \exists a \in A : a \prec y[/tex]
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