An Algorithm to Solve a Linear Program

This work is about an algorithm for solving a linear program which is simple to apply. There are three algorithms in this work. The first algorithm solves a two-variable linear program. This algorithm is built on simple concepts such as the slope and the intercept of a line. The core idea of the algorithm is the Deleting Principle based on the consistency between slopes and intercepts along the boundary of the feasible region. The second algorithm is the main algorithm. It solves a general linear program. The algorithm starts from the origin and moves to other points on the boundary of the feasible region. The algorithm depends on a two-dimensional intersection process: a systematic and repeated application of the first algorithm that will lead to a feasible solution on the boundary of the feasible region called a stable solution. The third algorithm or the judging algorithm is applied on every stable solution reached in the main algorithm. The judging algorithm either verifies that a stable solution is optimal or outputs a new feasible solution on the boundary. In the latter case, the judging algorithm shows how to get out of a trapped stable solution. The main algorithm may then be repeated by applying the first algorithm along the new direction suggested by the judging algorithm where the objective function is guaranteed to improve. Thus the main algorithm will eventually lead to a stable solution that is optimal, if the problem is feasible.