This paper presents a family of multiple access interference (MAI) suppression receivers based on the adaptive projected subgradient method. The proposed scheme can be applied to many different channel models and modulations in a unified manner. Moreover, it is suitable for both blind and nonblind receivers. The adaptive projected subgradient method realizes excellent convergence to a set including an optimal solution with high probability by asymptotically minimizing a sequence of nonnegative convex functions. Simulation results show much better (variable) tradeoff between speed and performance at steady-state as compared to existing techniques