Methods for calculatingl p -minimum norm solutions of consistent linear systems

Abstract

This paper describes, analyzes, and tests methods for solvingl p -minimum norm problems of the form $$\min \left\| x \right\|_p^p /p,s.t.Ax = b,$$ where 1 2 and a dual Newton method that is suitable when 1<p<2. Primaldual methods are also introduced. Numerical experiments illustrate the usefulness of the proposed methods.