The purpose of this paper is to introduce a new pivot rule of the simplex algorithm. The simplex algorithm first presented by George B. Dantzig, is a widely used method for solving a linear programming problem (LP). One of the important steps of the simplex algorithm is applying an appropriate pivot rule to select the basis-entering variable corresponding to the maximum reduced cost. Unfortunat...

We describe a cutting plane algorithm for solving linear ordering problems. The algorithm uses a primal-dual interior point method to solve the rst few relaxations and then switches to a simplex method to solve the last few relaxations. The simplex method uses CPLEX 4.0. We compare the algorithm with one that uses only an interior point method and with one that uses only a simplex method. We so...

We present a Simplex-type algorithm, that is, an algorithm that moves from one extreme point of the infinite-dimensional feasible region to another not necessarily adjacent extreme point, for solving a class of linear programs with countably infinite variables and constraints. Each iteration of this method can be implemented in finite time, while the solution values converge to the optimal valu...

L1 norm estimator has been widely used as a robust parameter estimation method for outlier detection. Different algorithms have been applied for L1 norm minimization among which the linear programming problem based on the simplex method is well known. In the present contribution, in order to solve an L1 norm minimization problem in a linear model, an interior point algorithm is developed which ...

This paper presents a new phase 1 simplex algorithm for solving linear programming problems. In the algorithm, first, the equation with the auxiliary objective function at the optimality as a new constraint is added to phase 1, and then a pivot is performed to generate one vertex on the associated objective hyperplane. This vertex may be feasible or not feasible. If it is feasible, the phase 1 ...

Ji et al. have conjectured that using the matrix form (to represent a basic solution) instead of the Simplex tableau in the dual Simplex method will lead to an algorithm with the time complexity comparable to the Hungarian algorithm for solving the Assignment Problem. In this note we show that both the time complexity and the CPU times of the Ji et al. algorithm are far away from being competit...