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A novel blind equalization method based on a subgradient search over a convex cost surface is examined under a noisy channel and a modification is proposed. This is an alternative to the existing iterative blind equalization approaches such as constant modulus algorithm (CMA) which mostly suffer from the convergence problems caused by their non-convex cost functions. The proposed method is an iterative algorithm, for both real and complex constellations, with a very simple update rule that minimizes the l∞ norm of the equalizer output under a linear constraint on the equalizer coefficients. The subgradient based algorithm has a fast convergence behavior attributed to the convex l∞ cost surface. A moving window based approach is used in this algorithm to both decrease the algorithm's complexity and increase its immunity to noise.