Solving Systems of Linear Equations and Inequalities

In this paper we present an algorithm which determines whether or not a system of linear equations and inequalities is consistent and if consistent, calculates a solution (feasible point) to it. This problem often occurs as a subproblem to a constrained optimization problem when the technique used to solve the optimization problem requires an initial feasible point. Also included is the convergence analysis, numerical examples and the results of tests comparing our algorithm with other methods for solving this problem.