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Transmitter optimization for correlated multiple input single-output (MISO) channels with average channel information feedback is of theoretical and practical importance. It was tackled in the past by mainly focusing on cases with either mean or covariance feedback alone. The difficulty with generic MISO optimization arises from the fact that the treatment of optimal beam directions and power allocation are no longer separable, thereby making the problem nearly impossible to be tackled on the basis of its current formulation. We therefore take a different philosophy by representing the derivative of the ergodic capacity as a single integral and linking it to the channel characteristic function. This new formulation allows us to obtain the sufficient and necessary conditions, simply in the form of two vector equations which can be efficiently solved by a Newton-Raphson type algorithm developed in this paper. Numerical results are presented for illustration.