In mathematical optimization, Wolfe duality, named after Philip Wolfe, is type of dual problem in which the objective function and constraints are all differentiable functions.
Using this concept a lower bound for a minimization problem can be found because of the weak duality principle.
[1] For a minimization problem with inequality constraints, the Lagrangian dual problem is where the objective function is the Lagrange dual function.
are convex and continuously differentiable, the infimum occurs where the gradient is equal to zero.
[2][clarification needed] This problem employs the KKT conditions as a constraint.
In any case, weak duality holds.