Question: 1. Consider the following problem: Minimize 3x} + 2x1x2 + 4x2 subject to - 3x1 2x2 + 6 = 0. a. Write the KKT necessary

1. Consider the following problem: Minimize 3x} +

1. Consider the following problem: Minimize 3x} + 2x1x2 + 4x2 subject to - 3x1 2x2 + 6 = 0. a. Write the KKT necessary conditions. b. Find a KKT point (x1, x2) and the Lagrange multiplier v associated with the constraint. c. Formulate the auxiliary function F(x1,x2) using the augmented Lagrangian penalty function with u = 1 and the Lagrange multiplier you found in (b). d. Is F(x1, x2) strictly convex? e. Analytically solve min F(x1,x2). Compare your solution to the solution in (b)

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