global optimum

A feasible x^* is a global minimum if f(x^*)\le f(x) for every feasible x, with no restriction to a neighborhood — the strongest possible claim a solution can make. Every global minimum is automatically a local minimum, but a local minimum need not be global; most of this course's algorithms are only guaranteed to find a local optimum unless the problem has extra structure (like convexity) ruling out the gap between the two.