This a simple example for optimization code using Augmented Lagrange Method
objective function : f (x,y) = (x-2)^2 + (y-2)^2
inequality constraint : g1(x,y) = 7-x-y <= 0 g2(x,y) = 1+x-y <= 0
initial condition : lambda1 = lambda2 = 0
Note : Correct solution => x* = [3.0 4.0] lambda = [3.0 1.0] f* = 5.0 g* = [0.0 0.0]