Consider the nonlinear optimization problem minimize mm + x3 subject to it] +x2 + (3(3)2 5 2 x1 2 0, x; Z 0. (a) Find the optimal solution and the multiplier corresponding to the nonlinear constraint. (b) Does the Lagrangian of this problem have a saddle point? (c) Form the augmented Lagrangian. For which values of the penalty param- eter does the duality relation hold true for the augmented Lagrangian in a neighborhood of the optimal solution