On the minimum-norm solution of convex quadratic programming

Abstract

We discuss some basic concepts and present a numerical procedure for finding the minimum-norm solution of convex quadratic programs (QPs) subject to linear equality and inequality constraints. Our approach is based on a theorem of alternatives and on a convenient characterization of the solution set of convex QPs. We show that this problem can be reduced to a simple constrained minimization problem with a once-differentiable convex objective function. We use finite termination of an appropriate Newton’s method to solve this problem. Numerical results show that the proposed method is efficient.