Fairness is an important concern in machine learning. One way to characterize the problem is to minimize some objective function, representing a quantity like loss, under constraints that represent fairness conditions like demographic parity. Previous papers show how a two-player approach to optimizing the Lagrangian can be computationally efficient and provably converge to a good, constraint-satisfying solution on convex objective functions. This work analyzes the convergence of the two-player framework in previous works on nonconvex functions, in particular those that satisfy the PL inequality.