In this paper, we present a novel and effective linearization technique for nonlinear phased array antennas. For large phased arrays, linearization of the array using a single digital predistortion (DPD) is inevitable since one digital path is upconverted and feeds several RF transmission paths, each of which is connected to a power amplifier (PA) and an antenna element. However, a critical issue is that the PA characteristics can vary considerably within an array. Thus, linearizing individual PAs with one DPD is rather challenging. We formulate and solve an optimization problem that corresponds to jointly minimizing the maximum residuals between the input to the array and the output of individual PAs. We demonstrate that the proposed technique outperforms state-of-the-art linearization solutions while retaining the linear gain of the array.