Free flight is an emerging paradigm in Air Traffic Management (ATM). Conflict detection and resolution is the heart of any free flight concept, and is the focus of this presentation. We address the problem of optimal cooperative three-dimensional (3D) conflict resolution involving multiple aircraft using rigorous numerical trajectory optimization methods. The conflict problem is posed as an optimal control problem of finding trajectories that minimize a certain objective function while maintaining the safe separation between each aircraft pair. We assume the origin and destination of the aircrafts are known and consider aircrafts models with simplified kinematics as well as detailed nonlinear point-mass dynamics. The protection zone around the aircraft is modeled to be cylindrical in shape. We propose a novel formulation of the cylindrical protection zone using continuous variables. The optimal control is converted to a finite dimensional Non Linear Program (NLP) using collocation on finite elements. We solve the NLP using an Interior Point algorithm that incorporates a novel line search method. Lastly, we also discuss some open problems of research interest in the above context.