We present a technique, based on the continuation method, to face power synthesis problems for array antennas. By using the least squares method (LSM), the power synthesis problem reduces to the minimization of an objective functional, which represents the square of the distance between the required and actual complex radiation pattern. Exploiting the Gram-Schmidt method (GSM) and the constrained minimization theory, the objective functional can be turned into a Lagrangian functional, which depends only on the radiation phase distribution. We use an iterative procedure for the optimization of the Lagrangian functional and we also introduce a continuation method to improve the reliability and robustness of the algorithm with respect to spurious solutions. Numerical simulations show better performance of the proposed algorithm, in terms of mean square error, than iterative least square synthesis (ILSS), although a slightly higher computational effort is required.