A new method for blind equalization is proposed which changes the cost function of the equalizer as the convergence proceeds. Motivation for this idea is given by tests of the new "uniform optimum" O/sub /spl infin///sup 2/ cost function for blind equalization proposed in Satorius and Mulligan (1993), comparing it to the more familiar O/sub 4//sup 2/ Godard-like cost. The new cost achieves better asymptotic performance than O/sub 4//sup 2/ for communications data, but has a zero tracking ability measure, this being an example of the tracking/accuracy compromise of adaptive algorithms. This suggests the use of a sliding cost function algorithm which monitors the convergence state of the equalizer. The sliding cost function algorithm is developed as a "maximum a posteriori (MAP) estimate of the blind gradient" method for blind equalization which assumes the the data fit a generalized Gaussian distribution model. The model parameters are updated at each iteration, and the algorithm adapts its cost function so as to have good tracking ability while converging, and optimal steady state performance at convergence.