We introduce two support vector machine (SVM)-based approaches for solving antenna problems such as beamforming, sidelobe suppression, and maximization of the signal-to-noise ratio. A basic introduction to SVM optimization is provided and a complex nonlinear SVM formulation developed to handle antenna array processing in space and time. The new optimization formulation is compared with both the minimum mean square error and the minimum variance distortionless response methods. Several examples are included to show the performance of the new approaches