Exhibit a constrained optimization problem that has only one local minimum, such that (a) at least one Lagrange multipler is nonzero, and (b) the local minimum is not a global minimum but satisfies...

Exhibit a constrained optimization problem that has only one local

minimum, such that (a) at least one Lagrange multipler is nonzero, and (b)

the local minimum is not a global minimum but satisfies the KKT conditions. Show that the local minimum fails the sufficient conditions for a global

minimum.