New Algorithm for System of Linear Inequalities

A pivoting-based algorithm for the system of linear inequalities is proposed. Since it solves the system directly without adding any variables, a compact form is used for operations. It not only requires less computation for each iteration but also makes easy the theoretical analysis for the characteristics of the solved problem. It is proved that this method terminates as long as the entering and leaving variables are selected by the smallest-subscript rule in each iteration. This proof is essentially that proposed by G.B. Bland, but varies greatly in the form. The experiment shows that this method is very efficient for solving Markowitz's portfolio selection model (convex quadratic programming).