The optimum bit detector for multiuser CDMA systems has an exponential complexity in the number of users. Many suboptimum receivers have been developed to achieve good performance with less complexity. We approximate the solution of the optimum multiuser detection problem using nonlinear programming relaxations. We observe that some popular suboptimum receivers correspond to relaxations of the optimal detection problem. In particular, one approximation method yields to iterative solutions which correspond to previously proposed heuristic nonlinear detectors. We identify the convergence properties of these iterative detectors. We also propose a relaxation that yields a receiver which we call the generalized MMSE detector. We give a simple iterative implementation of the detector. Its performance is evaluated and comparisons to other suboptimum detection schemes are given.