A general phase-I method in linear programming

The basic technique for solving LP problems is still the simplex method [2]. It has many variants but in practice the primal simplex methods are considered the most important. Phase I of the primal methods serves for finding a basic feasible solution but the same procedure can also be used for generating feasible points of other problems with linear constraints, or even for checking the consistency of a system of linear equalities/inequalities. Since in Phase I the objective function is not or only slightly considered it usually does not move towards optimality. It would be advantageous if Phase I were as short as possible or if it could better take into account the real objective function. In this paper we try to contribute to both of these aspects positively