An Algorithm for Minimum L-Infinity Solution of Under-determined Linear Systems

This paper presents a primal method for finding the minimum L-infinity solution to under-determined linear systems of equations. The method is a two-phase method. Line search is performed at both phases. We establish a condition for a direction to be descent. The convergence proof of the method is shown. Expedient numerical schemes can be used whenever appropriate. Results are presented, which show the superiority of the method over some well-known methods.