4. [10 points] (Dual of a Convex Program) Consider the following optimization problem: minimizesubjecttox12+x2214x16x2+27x1+x22x1+2x23 It can be shown using the KKT conditions that the global minimum of this optimization problem is given by x=(3,1) with the corresponding Lagrange multiplier vector =(8,0). (You may verify if you like.) (a) Find the dual of this optimization problem. (b) Show that the strong duality holds. 4. [10 points] (Dual of a Convex Program) Consider the following optimization problem: minimizesubjecttox12+x2214x16x2+27x1+x22x1+2x23 It can be shown using the KKT conditions that the global minimum of this optimization problem is given by x=(3,1) with the corresponding Lagrange multiplier vector =(8,0). (You may verify if you like.) (a) Find the dual of this optimization problem. (b) Show that the strong duality holds