An Algorithm For A Minimum Norm Solution Of A System Of Linear Inequalities

A common problem encountered in the studies of the least squares problems is that of finding the minimum Ê 2 norm solution of a system of linear equations. In this paper, we consider an algorithm for computing the vector of minimum norm solution of a given system of linear inequalities. We replace the Ê 2 norm by $\ell^p\comma \, 1\lt p \lt\infty$ . Duality theorems and characterizations of the solution are given. The feasibility of the method is proved and some numerical experimentations are included.

Keywords:

• Minimum Norm Solution
• Linear Inequalities
• Residual
• Smooth Strictly Convex Norm
• Least Distance Algorithm