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

(a) Consider the following non-linear optimization program P : If (x)] subject to : g (x) =0 max h(x) 20 ' (1) where f : R"- R, g : R" - R", and h : R"- 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) = 21 + 12 and g(x) = ] + 30112 + 3.17 -3. (2)

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