Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2009.3402.3406NavidiH.MalekA.KhosraviP.122009918The aim of this study is to find an exact least 2-norm solution to a primal constrained linear programming problem in the standard form. Moreover, we can generate an exact solution to the dual programming problem using the exact least 2-norm solution to the primal problem. The proposed algorithm is suitable for solving linear programming problems with a very large number of variables (10^{5}) and a very large number of constraints (10^{6}). The exact least 2-norm solution to the primal problem is based on the minimization of exterior penalty functions dual of the dual programming problem. In practice for minimization, we use generalized Newton method and strong wolf conditions in order to find a corresponding suitable step size. This hybrid algorithm converges to the correct optimal solution independent of the values of the given starting point. It is shown that there are some problems that without using strong wolf conditions cannot be solved. The new algorithm can obtain least solution in comparison with MATLAB. Numerical results for a subset of problems from the Netlib collection and a subset of generated large scale linear programs are given. The hybrid algorithm is easy to implement and computationally very efficient. Comparisons are made with available literature.]]>Evtushenko-Yu, G., A.I. Golikov, S. Ketabchi and N. Mollaverdi,2004Fischer, A. and C. Kanzow,1996Golikov A.I. and Y.G. Evtushenko,2000Ketabchi, S., H. Navidi and N. Mollaverdi,2009Luca, T.D., F. Facchinei and C. Kanzow,1996Mangasarian, O.L.,1995Mangasarian, O.L.,2002Mangasarian, O.L. and R.R. Meyer,1979Rao, S.S.,1984