Modified Simplex Splitting Algorithm for Finding Feasible Solution of Systems of Linear Inequalities

Abstract

In this paper the existing simplex splitting algorithm for finding a feasible solution of systems of linear inequalities is modified by evolving a vertex-determination technique. The existing algorithm cannot determine when the system of linear inequalities is infeasible hence the need for a modification. The modified algorithm is able to determine the feasible solution whenever it exists and to detect infeasibility whenever it occurs. The modified algorithm is tested on a problem that has a feasible solution and also on a problem that has no feasible solution and is found to work perfectly well.