This paper presents two novel blind set-theoretic adaptive filtering algorithms for suppressing" Multiple Access Interference (MAI)," which is one of the central burdens in DS/CDMA systems. We naturally formulate the problem of MAI suppression as an asymptotic minimization of a sequence of cost functions under some linear constraint defined by the desired user's signature. The proposed algorithms embed the constraint into the direction of update, and thus the adaptive filter moves toward the optimal filter without stepping away from the constraint set. In addition, using parallel processors, the proposed algorithms attain excellent performance with linear computational complexity. Geometric interpretation clarifies an advantage of the proposed methods over existing methods. Simulation results demonstrate that the proposed algorithms achieve (i) much higher speed of convergence with rather better bit error rate performance than other blind methods and (ii) much higher speed of convergence than the non-blind NLMS algorithm (indeed, the speed of convergence of the proposed algorithms is comparable to the non-blind RLS algorithm).