One of the difficulties when dealing with nonconvex or NP-complete optimization problems is that one often falls into local optima. When this happens, often the global optimum is then impossible to reach. In figure 1a there is a convex solution space. Here there are no local optima, just a global optimum. In figure 1b however we have a space with lots of local optima (the pyramid tops). If an algorithm gets stuck on one of these it is possible that it will stay there.