Duality gap

In optimization problems in applied mathematics, the duality gap is the difference between the primal and dual solutions. If ${\displaystyle d^{*}}$ is the optimal dual value and ${\displaystyle p^{*}}$ is the optimal primal value then the duality gap is equal to ${\displaystyle p^{*}-d^{*}}$. This value is always greater than or equal to 0 (for minimization problems). The duality gap is zero if and only if strong duality holds. Otherwise the gap is strictly positive and weak duality holds.

...
Wikipedia