A new efficient primal dual simplex algorithm

Authors:
Konstantinos Paparrizos;Nikolaos Samaras;George Stephanides
Affiliations:
Department of Applied Informatics, University of Macedonia, 156 Egnatia Str., POB 1591, 54006 Thessaloniki, Greece;Department of Applied Informatics, University of Macedonia, 156 Egnatia Str., POB 1591, 54006 Thessaloniki, Greece;Department of Applied Informatics, University of Macedonia, 156 Egnatia Str., POB 1591, 54006 Thessaloniki, Greece
Venue:
Computers and Operations Research
Year:
2003

Citing 5
Cited 4

A new polynomial-time algorithm for linear programming

Combinatorica
An infeasible (exterior point) simplex algorithm for assignment problems

Mathematical Programming: Series A and B
Multiple centrality corrections in a primal-dual method for linear programming

Computational Optimization and Applications
Combining interior-point and pivoting algorithms for linear programming

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

Operations Research Letters

An improved intial basis for the simplex algorithm

Computers and Operations Research
A deficient-basis dual counterpart of Paparrizos, Samaras and Stephanides' primal-dual simplex-type algorithm

Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART II
The impact of scaling on simplex type algorithms

Proceedings of the 6th Balkan Conference in Informatics
Combining interior and exterior simplex type algorithms

Proceedings of the 17th Panhellenic Conference on Informatics

Quantified Score

Hi-index	0.01

Visualization

Abstract

The purpose of this paper is to present a revised primal dual simplex algorithm (RPDSA) for linear programming problems. RPDSA has interesting theoretical properties. The advantages of the new algorithm are the simplicity of implementation, low computational overhead and surprisingly good computational performance. The algorithm can be combined with interior point methods to move from an interior point to a basic optimal solution. The new algorithm always proved to be more efficient than the classical simplex algorithm on our test problems. Numerical experiments on randomly generated sparse linear problems are presented to verify the practical value of RPDSA. The results are very promising. In particular, they reveal that RPDSA is up to 146 times faster in terms of number of iterations and 94 times faster in terms of CPU time than the original simplex algorithm (SA) on randomly generated problems of size 1200 × 1200 and density 2.5%.