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Convex combination and lp's

  1. Feb 11, 2009 #1
    1. The problem statement, all variables and given/known data

    The question is "Show that in the case of any linear program, every convex combination of optimal extreme points is optimal."

    2. Relevant equations

    ok so if (x_1,....,x_n) is a list of the optimal points then
    a_1(x_1)+ .....+a_n(x_n) is the convex combination st a_i>0 and sum of a's is 1

    so the convex combination spans the list of optimal points.
    their dimensions are the same so the convex combination is a basis for the optimum points...

    3. The attempt at a solution

    is this the right idea, i don't see how to show EVERY convex combinaiton is optimal
  2. jcsd
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