A new method for solving a linear programming problem

This paper presents a new method for solving a linear programming problem, which is an extended version of the one previously presented by the author. The optimal solution of a linear programming problem is composed of some inequality constraints in their equality form. Then, it is possible to recognize the problem of finding the equality constraints which constitute the optimal solution. Some index is introduced to estimate the equality constraints among the inequality conditions. The estimated constraints give some solution which may be optimal or not optimal but feasible solution, or infeasible solution. Then the remains of the algorithm are the methods to transfer the infeasible/feasible solution to a feasible/optimal solution. Some candidate algorithm with a new optimality criterion is proposed in this paper and is confirmed its validity by many examples. The algorithm is also applied for solving a traveling salesperson problem.