The problem of recognition in nonparametric environments under imperfect supervision is not amenable to solution through classical statistical approaches based on identification of finite mixtures, which require an a priori knowledge of the probabilistic descriptions of the classes. Accordingly, the problem is viewed in this study as one of optimal linear/nonlinear partitioning of the imperfectly labeled training sample set. This optimal partitioning is accomplished by defining an appropriate optimality criterion, which takes into account the imperfectness of supervision, and solving the resultant optimization problem through the Improved Flexible Polyhedron Method (IFPM). Possible alternatives to compensate for the inherent bias in this criterion towards equipopulation clusters are developed and evaluated using an illustrative example. Details of the methodology involved in implementing the approach are presented. Results of simulation experiments, which confirm the validity and effectiveness of this new technique in accomplishing optimal, linear/nonlinear discriminant learning in imperfectly supervised, nonparametric environments, are included.