Say you have a city with two skyscrapers on opposite sides of town, one 49 stories high and the other 51 stories high. When you're at the top of the 49-story building, you're at a local maximum of height and close to the global maximum, but you're not exactly a short gradient-ascent jaunt away from the global maximum.
Sure, but how much work are you going to put in to go up two floors? Local optimum + close to a global optimum means there's not much cost benefit in changing.
