Feasibility issues in primal-dual interior-point method for linear programming

A new method for obtaining an initial feasible interior-point solution to a linear program is presented. This method avoids the use of a ‘big-M’, and is shown to work well on a standard set of test problems. Conditions are developed for obtaining a near-optimal solution that is feasible for an associated problem, and details of the computational testing are presented. Other issues related to obtaining and maintaining accurate feasible solutions to linear programs with an interior-point method are discussed. These issues are important to consider when solving problems that have no primal or dual interior-point feasible solutions.