The estimation of an inner-linearized approximation to a general convex or concave function with n independent variables is formulated as a concave programming problem. An algorithmic procedure, based on relaxation, which generates constraints as required is proposed. Both the formulation and solution procedure hold for an arbitrary norm. When the least squares norm is used, the estimators are shown to be consistent. An example shows that when n=l the general formulation reduces to the single independent variable formulation suggested by Dent and the proposed algorithm automatically generates the subset of Dents constraints required to obtain the optimal estimators.