Consider the quadratic programming problem

1-Solve the problem using KKT conditions.
2-Observe that, if we could get rid of the first inequality, we could decompose the problem into two independent minimizations with respect to each variable. Hence, dualize the coupling constraint, find the dual function, and check that the maximum of the dual function is the same as the optimal value of the primal.

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min x+x + s.t. x1 x24, x1, x2 0.