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In this paper the problem of blind equalization of constant modulus (CM) signals is formulated within the support vector (SV) regression framework. The quadratic inequalities derived from the CM property are transformed into linear ones, thus yielding a quadratic programming (QP) problem. Then an iterative reweighted procedure is proposed to blindly restore the CM property. The technique can be generalized to nonlinear blind equalization using kernel functions. We present simulation examples showing that linear and nonlinear blind SV equalizers offer better performance than cumulant-based techniques, mainly in applications when only a small number of data samples is available, such as in packet-based transmission over fast fading channels.