A systematic treatment of well-known optimization problems in which an active set strategy leads to a finite algorithm. Applies techniques of convex analysis to problems in convex and nonconvex programming involving polyhedral functions. An important contribution of this work is the derivation of a compactly parametrized representation of the subdifferential of a polyhedral convex function. Develops finite algorithms for robust statistical estimators, nonparametric estimators based on rank, and errors in variables problems. Gives a detailed discussion of the basic solution procedures for the simplest case (the linear programming problem) and includes a treatment of degeneracy. Provides a model for subsequent developments such as quadratic programming, M-estimation, and total approximation.