Question: Consider the following convex programming problem: Maximize f(x) 10x1 2x1 2 x1 3 8x2 x2 2 , subject to x1 x2 2

Consider the following convex programming problem:

Maximize f(x) 10x1  2x1 2  x1 3 8x2  x2 2

, subject to x1 x2 2 and x1  0, x2  0.

(a) Use the KKT conditions to demonstrate that (x1, x2) (1, 1)

is not an optimal solution.

(b) Use the KKT conditions to derive an optimal solution.

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