Question: (a) Consider the following non-linear optimization program P : max f (x)] subject to : g (x) = 0 h(2 ) 20 ' (1) where

(a) Consider the following non-linear optimization program P : max f (x)] subject to : g (x) = 0 h(2 ) 20 ' (1) where f : Rn - R, g : Rn- Rm, and h : Rn - R* are smooth functions. Carefully state the Karush-Kuhn-Tucker (KKT) theorem as it applies to P. (b) Use the KKT theorem to find the solution to the special case of P above where f : R2 _> R and g : R2-> R are defined by: f(x) = x1 + 2 and g(x) = x1 + 3x122 + 3x2 - 3. (2)

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