Homework Help: Kkt theorem (minimization)

1. Dec 12, 2009

hoffmann

what does it mean to write out the kkt conditions and find x* for the following problem:

minimize $$f(x) = \sum x_i$$ subject to $$\prod x_i = 1$$ and $$x_i \geq 0$$ for 1<= i <= n. the bounds on the sum and product are from i = 1 to n.

2. Dec 13, 2009

HallsofIvy

Well, what is the "kkt" (Karush–Kuhn–Tucker) theorem?

3. Dec 13, 2009

hoffmann

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.