Computational experiments were performed with a primal-dual algorithm, using surrogate objective functions to solve the linear programming problem. Three different rules for switching between the primal and the dual problem and seven different ways to construct the surrogate objective function were used to solve 28 LP problems. For the moment it seems that the sum of the infeasibilities is the best indicator for attacking either the primal or the dual problem and that the sum of the violated constraints is the best surrogate objective function, judging by the number of iterations. . On the other.hand this version is shown to be not necessarily finite, while the other switching rules yield finite procedures. However, in Oneral the primal-dual surrogate simplex method clearly outperforms the twophase simplex method.