In
mathematical optimization theory,
duality means that
optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem (the
duality principle). The solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem. However in general the optimal values of the primal and dual problems need not be equal. Their difference is called the
duality gap. For
convex optimization problems, the duality gap is zero under a
constraint qualification condition.