This paper presents sufficient conditions for optimality of the Linear programming (LP) problem in the neighborhood of an optimal solution, and applies them to an interior point method for solving the LP problem. We show that after a finite number of iterations, an exact solution to the LP problem is obtained by solving a linear system of equations under the assumptions that the primal and dual problems are both nondegenerate, and that the minimum value is bounded. If necessary, the dual solution can also be found.
