Dual problem

What's the point of dual problem?
Dual problem can be very helpful for defining a lower bound on the minimum value of a function. Note that the primal problem does not have to be convex; in fact, the dual can be more informative in such cases as it may allow us to know how far from the optimum (that we'll probably be unable to reach -- because the problem is not convex and we have to go for local optima etc.) are.