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If the desired signal is present in training snapshots, the adaptive array performance is known to be quite sensitive even to slight mismatches between the presumed and actual signal steering vectors. Such mismatches can occur as a result of environmental nonstationarities, look direction errors, imperfect array calibration or distorted antenna shape, as well as distortions caused by medium inhomogeneities, near-far mismatch, source spreading, and local scattering. The similar type of performance degradation can occur when the signal steering vector is known exactly but the training sample size is small. In this paper, we develop a new approach to robust adaptive beamforming in the presence of an arbitrary unknown signal steering vector mismatch. Our approach is based on the optimization of worst-case performance using Second-Order Cone (SOC) programming. The adaptive beamformer proposed is shown to have a substantially improved robustness as compared to existing algorithms and enjoy simple implementation.