View article

The problem of minimizing a quadratic function with linear inequality constraints is considered with applications to nonparametric regression with shape assumptions. For many problems, the set defined by the constraints is a closed convex cone. The mixed primal–dual bases algorithm (Fraser and Massam, 1989, Scand. J. Statist. 16, 65–75) for regression under inequality constraints finds a least-squares regression estimate over such a cone in a finite number of steps, with the restriction that the number of constraints does not exceed the number of dimensions in the space. Some applications, however, require more constraints than dimensions, and the main purpose of this paper is to extend the algorithm to this more general case. Properties of the constraint cone and its polar cone are presented in the generality necessary in this situation. One surprising result is that the number of generators of the constraint cone …