The surface is called a hyperbolic paraboloid. Notice that it looks like a saddle: part convex surface and part concave. In the figure above, we start descending from our location and ostensibly reach a place where the gradient is zero. But this is an unstable place. It’s called a saddle point. One false step, and you’ll tumble down the surface. This function has no global or local minimum. Also, the initial starting point can dictate whether you even come close to the saddle point while descending.
