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Robust adaptive beamforming is a challenging task in wireless communications due to the strict restrictions in the number of available snapshots, signal mismatches, or calibration errors. We present a new approach to adaptive beamforming that provides increased robustness against the mismatch problem as well as some control over the sidelobe level. We modify the conventional Capon cost function by including a regularization term that penalizes differences between the actual and the target (ideal) array responses. By using the so-called e-insensitive loss function as the penalty term, the cost function adopts the form of a support vector machine for regression. In particular, the resulting cost function is convex with a unique global minimum that can be efficiently found using quadratic programming techniques. Simulation examples show the performance of the proposed SVM-based beamformer when it is compared with traditional and other robust beamforming techniques.