Question 2: Consider the problem: min (21 - 0.5)2 + (12 + 0.5) 2 subject to 4x1 + 2x2 5 0, (1) x1 + 2 21, x2 2 0. Q2.a Describe the tangent cone to the feasible set at the point (-1, 2). Solution The first two constraints are active at that point. Therefore, the tangent cone is T(-1,2) = {de R2 : 4d1 + 2d2 > 0 with the constraint 4x1 + 2x2 5 0, a multiplier / > 0 with -21 - 12 + 1 0, {dER? : d1 = 0, d2 0} if x2 = 0. The Lagrange function of this problem is: L(x, A, H) = (21 - 5)2 + (262 + 5)2 + X(4x1 + 212) -14(21+2:2 -1). The optimality conditions are