WE continue our consideration of optimization problems by studying the constrainedcase. These problems take the following general form: minimize f(~x)
subject to g(~x) = ~0
h(~x) ≥ ~0.
Here, f : Rn → R, g : Rn → Rm, and h : Rn → Rp; we call f the objective function and the expressions g(~x) = ~0, h(~x) ≥ ~0 the constraints.