A Reduced-Order Correction Algorithm for the Linear Programming Problem by Non-negative Constraints with the Most-Obtuse Angle

Abstract

Based on the linear and geometric-plane features of linear programming, and the consistent quantity of null-elements for all the non-degenerate base-solutions of some linear programming problem, with the help of the new platform, constructed by the conceptions including characteristic matrix of linear programming problem, negative pivoting iteration transformation and so on, a new solution method, named as reduced-order correction algorithm by nonnegative constraints with the most-obtuse angle, is proposed in this paper. At the same time, a -regularization method is given to avoid basis-circulating problem, which maybe take place for the reason of the degenerate phenomenon, in the process of solving linear programming. Comparing with the Simplex Method, the instance shows that it is more highly efficient for us to apply this new method to solving the linear programming proble