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Homework Help: Kkt theorem (minimization)

  1. Dec 12, 2009 #1
    what does it mean to write out the kkt conditions and find x* for the following problem:

    minimize [tex]f(x) = \sum x_i[/tex] subject to [tex]\prod x_i = 1[/tex] and [tex]x_i \geq 0[/tex] for 1<= i <= n. the bounds on the sum and product are from i = 1 to n.
     
  2. jcsd
  3. Dec 13, 2009 #2

    HallsofIvy

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    Well, what is the "kkt" (Karush–Kuhn–Tucker) theorem?
     
  4. Dec 13, 2009 #3
    basically the kkt conditions need to be satisfied if the solution is optimal. you have the two constraints as your functions (say g and h) -- both these and the objective function need to be stationary, dual and primal feasible, and satisfy complementary slackness.

    anyway, so i think there are two cases for the product to be equal to one: one is when all the x_i are equal to 1 and the other is when the product of the x_i's somehow approaches 1. in the first case, the sum would just give n since all the x_i's equal 1, and the second case...well i'm not so sure.

    am i thinking about this problem in the right way?
     
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