Free flight is an emerging paradigm in Air Traffic Management (ATM). In this paper, we focus on the problem of cooperative 3D conflict resolution among multiple aircraft by posing it as an optimal control problem of finding trajectories that minimize a certain objective function while maintaining safe separation between each aircraft pair. We assume the origin and destination of the aircraft are known and consider aircraft models with detailed nonlinear point-mass dynamics. The protection zone around the aircraft is modeled to be cylindrical in shape. We also extend the modeling framework to accommodate no-fly zones of finite height or otherwise. A novel formulation of the cylindrical protection zone using continuous variables. We address the solution of this problem using rigorous numerical trajectory optimization methods. The optimal control problem is converted to a finite dimensional NonLinear Program (NLP) using collocation on finite elements. We solve the NLP using an Interior Point algorithm that incorporates a novel line search method. We also propose a reliable initialization strategy that yields a feasible solution on simple models and is also adapted to detailed models. Resolution scenarios including cases with no-fly zones are illustrated.