Consider the NLP min 151x122 + 41x222 s.t. 3x1 + 2x2 = 8 x1, x2 0

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Consider the NLP min 151x122 + 41x222 s.t. 3x1 + 2x2 = 8 x1, x2 Ú 0

(a) State the KKT optimality conditions for this model.

(b) Verify that at solution x = 10, 42 there exists an improving feasible direction

x = 12, -32.

(c) Confirm that KKT conditions have no solution for the nonoptimal x of part (b).

(d) Explain why every local optimum of the model must be a KKT point.

(e) Show that global optimal solution x* =

11, 52 2 is a KKT point.

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