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Adaptive beamforming methods degrade in the presence of both signal steering vector errors and interference nonstationarity. We develop a new approach to adaptive beamforming that is jointly robust against these two phenomena. Our beamformer is based on the optimization of the worst case performance. A computationally efficient convex optimization-based algorithm is proposed to compute the beamformer weights. Computer simulations demonstrate that our beamformer has an improved robustness as compared to other popular robust beamforming algorithms.