This paper focuses on the conflict detection and resolution (CDR) of unmanned aerial vehicles (UAVs). Firstly, the airspace conflict problem of UAVs is studied and a taxonomy of conflict situation is presented. The multi-UAV conflict is studied in virtue of the graph theory. The CDR problem is casted to a nonlinear optimization problem. Secondly, a two layered optimization algorithm, which combines stochastic parallel gradient descent (SPGD) method and Sequential quadratic programming (SQP) algorithm, is presented to solve the nonlinear optimization problem. Numerical simulations are performed to demonstrate the computational efficiency of this solver. Thirdly, the proposed algorithm is extended to 3-D space. Finally, the proposed algorithm is demonstrated on several scenarios. The results demonstrate that the proposed method outperform the existing algorithms. It can obtain conflict free solutions that would not lead to unnecessary detors.@en