Abstract: A duality relation between the downlink max-min Signal-to-Interference-Noise Ratio (SINR) optimization issue and the virtual uplink min-max SINR optimization issue is revealed by using the Lagrange duality theory for coordinated multiple point joint transmission multiple input single output interference downlink system subject to per-base station power constraints. Based on the duality relation and subgradient theory, a two layer alternating iterative optimization beamforming method is proposed to solve the virtual uplink min-max SINR optimization issue. And the convergence of the proposed algorithm is proven. The complexity of the proposed method is analyzed by using real floating-point operation theory. Numerical simulation verifies the validity of the proposed method.