Consider the following linearly constrained convex programming problem:

Maximize f(x)
3x1  4x2  x1 3  x2 2

, subject to x1  x2 1 and x1 0, x2 0.

(a) Starting from the initial trial solution (x1, x2)
(

1 4

, 

1 4

), apply three iterations of the Frank-Wolfe algorithm.

(b) Use the KKT conditions to check whether the solution obtained in part

(a) is, in fact, optimal.