# On anti-cycling pivoting rules for the simplex method

@article{Zhang1991OnAP, title={On anti-cycling pivoting rules for the simplex method}, author={Shuzhong Zhang}, journal={Oper. Res. Lett.}, year={1991}, volume={10}, pages={189-192} }

A new anti-cycling pivoting rule for the simplex method is presented. A general framework for anti-cycling pivoting rules is proposed and investigated.

#### Topics from this paper

#### 20 Citations

New variants of finite criss-cross pivot algorithms for linear programming

- Mathematics, Computer Science
- Eur. J. Oper. Res.
- 1999

The finiteness of the new criss-cross pivot variants is proven and the so-called first-in-last-out pivot rule and the most-often-selected-variable pivot rule for the simplex method are generalized. Expand

Systematic construction of examples for cycling in the simplex method

- Mathematics, Computer Science
- Comput. Oper. Res.
- 2006

We present systematic procedures to construct examples of linear programs that cycle when the simplex method is applied. Cycling examples are constructed for diverse variants of pivot selection… Expand

An exterior point simplex algorithm for (general) linear programming problems

- Mathematics, Computer Science
- Ann. Oper. Res.
- 1993

An exterior point simplex type algorithm is presented that possesses a new monotonic property and cycling-free pivoting rules and an exponentional example are presented. Expand

A Monotonic Build-Up Simplex Algorithm for Linear Programming

- Mathematics, Computer Science
- Oper. Res.
- 1994

A new simplex pivot rule is devised which produces a sequence of pivots such that ultimately the originally chosen nonbasic variable enters the basis, and all reduced costs which were originally nonnegative remain nonnegative. Expand

Pivoting Rules for the Revised Simplex Algorithm

- Mathematics
- 2014

Pricing is a significant step in the simplex algorithm where an improving non-basic variable is selected in order to enter the basis. This step is crucial and can dictate the total execution time. In… Expand

Criss-cross methods: A fresh view on pivot algorithms

- Mathematics, Computer Science
- Math. Program.
- 1997

A recent result on the existence of a short admissible pivot path to an optimal basis is given, indicating shortest pivot paths from any basis might be indeed short for criss-cross type algorithms. Expand

Finite Pivot Algorithms and Feasibility

- Mathematics
- 2001

I RESUMÉ II ACKNOWLEDGEMENTS IV LIST OF TABLES VII LIST OF EQUATIONS VIII LIST OF FIGURES IX

GPU accelerated pivoting rules for the simplex algorithm

- Computer Science
- J. Syst. Softw.
- 2014

These results showed that the proposed GPU implementations of the pivoting rules outperform the corresponding CPU implementations. Expand

A Survey on Pivot Rules for Linear Programming

- Economics
- 1992

3 : Abstract The purpose of this paper is to survey the various pivot rules of the simplex method or its variants that have been developed in the last two decades, starting from the appearance of the… Expand

Resolution of the problem of degeneracy in a primal and dual simplex algorithm

- Mathematics, Computer Science
- Oper. Res. Lett.
- 1997

The problem of degeneracy is resolved in a recently developed primal-dual simplex algorithm for general linear programming problems and it is shown that the algorithm cycles. Expand

#### References

SHOWING 1-2 OF 2 REFERENCES

New Finite Pivoting Rules for the Simplex Method

- Mathematics, Computer Science
- Math. Oper. Res.
- 1977

A simple proof of finiteness is given for the simplex method under an easily described pivoting rule. A second new finite version of the simplex method is also presented.

Notes on Bland’s pivoting rule

- Mathematics
- 1978

Recently R.G. Bland proposed two new rules for pivot selection in the simplex method. These elegant rules arise from Bland’s work on oriented matroids; their virtue is that they never lead to… Expand