Use the KKT conditions to check whether the solution you obtained in part (b) is, in fact, optimal. If not, use these conditions to derive the exact optimal solution.

1. Consider the following linearly constrained convex programming problem: Maximize f (x) _ 4×1 _ x1
4                2×2 _ x2

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2,
subject to
4×1            2×2 _ 5
and
x1 _ 0, x2 _ 0.
(a) Starting from the initial trial solution (x1, x2) _ (
1
2
,
1 2), apply four iterations of the Frank-Wolfe algorithm.
(b) Show graphically how the sequence of trial solutions obtained in part (a) can be extrapolated to obtain a closer approximation of an optimal solution. What is your resulting estimate of this solution?
(c) Use the KKT conditions to check whether the solution you obtained in part (b) is, in fact, optimal. If not, use these conditions to derive the exact optimal solution.