Strong duality
Strong duality is a condition in mathematical optimization in which the primal optimal objective and the dual optimal objective are equal. By definition, strong duality holds if and only if the duality gap is equal to 0. This is opposed to weak duality.
Sufficient conditions
Each of the following conditions is sufficient for strong duality to hold:- where is the perturbation function relating the primal and dual problems and is the biconjugate of
- is convex and lower semi-continuous
- the primal problem is a linear optimization problem
- Slater's condition for a convex optimization problem.