Question: Consider the equality-constrained quadratic program min 61x122 + 21x222 - 6x1x2 + 41x322 + 5x1 + 15x2 - 16x3 s.t. x1 + 3x2 - 2x3

Consider the equality-constrained quadratic program min 61x122 + 21x222 - 6x1x2 + 41x322

+ 5x1 + 15x2 - 16x3 s.t. x1 + 3x2 - 2x3 = 2 3x1 - x2 + x3 = 3

(a) Identify the Q,

c, A, and b of (symmetric)

quadratic program standard form.

(b) State Karush–Kuhn–Tucker optimality conditions for the model as a system of linear equalities.

(c) Solve your system of part

(b) for the unique KKT point of the model.

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