We present a new method, blind EVM minimization, for constellation recovery and transmitter impairment evaluation of dual polarization optical signals with complex modulation formats. Using simulated data, for which transmitter impairments are known exactly, the method is shown to be accurate and robust. In addition, the method is successfully tested on measured QPSK and QAM16 data. Because of its relatively long run-time, the method might best be used for defining and measuring transmitter impairments and for judging the performance of faster constellation recovery methods that rely on serial parameter evaluation rather than optimization.