Question: Question 4 Consider following optimisation problem: 1 f(x) = 2x1x2 +5 x2 21-n x2 2x - 12/24 Minimise subject to [30 marks] (a) (5

Question 4 Consider following optimisation problem:[30 marks]Minimisef(x) = 5x1x2 + 5subject toX2 21-1112 224,-(a) (5

Question 4 Consider following optimisation problem: 1 f(x) = 2x1x2 +5 x2 21-n x2 2x - 12/24 Minimise subject to [30 marks] (a) (5 marks) Write down the Karush-Kuhn-Tucker (KKT) conditions for this problem. (b) (10 marks) Find the one feasible extremal point that satisfies the KKT conditions. (c) (5 marks) Find the tangent space of the active constraint at this point. (d) (10 marks) By applying the second-order condition, show that the extremal point obtained in (b) is not a local minimiser.

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a The KarushKuhnTucker KKT conditions for this problem can be written as follows 1 Stationarity condition fx gx gx 0 2 Primal feasibility gx 0 gx 0 3 Dual feasibility 0 0 4 Complementary slackness gx ... View full answer

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