A least-squares primal-dual algorithm for solving linear programming problems

2002 ◽  
Vol 30 (5) ◽  
pp. 289-294 ◽  
Author(s):  
Earl Barnes ◽  
Victoria Chen ◽  
Balaji Gopalakrishnan ◽  
Ellis.L. Johnson
Keyword(s):  
Linear Programming ◽  
Least Squares ◽  
Dual Algorithm ◽  
Primal Dual ◽  
Linear Programming Problems

ON SOLVING SHORTEST PATHS WITH A LEAST-SQUARES PRIMAL-DUAL ALGORITHM

2008 ◽  
Vol 25 (02) ◽  
pp. 135-150
Author(s):  
I.-LIN WANG
Keyword(s):  
Linear Programming ◽  
Least Squares ◽  
Shortest Path ◽  
Shortest Paths ◽  
Arc Length ◽  
Dual Algorithm ◽  
Shortest Path Problems ◽  
Dijkstra's Algorithm ◽  
Primal Dual ◽  
Linear Programming Problems

Recently a new least-squares primal-dual (LSPD) algorithm, that is impervious to degeneracy, has effectively been applied to solving linear programming problems by Barnes et al., 2002. In this paper, we show an application of LSPD to shortest path problems with nonnegative arc length is equivalent to the Dijkstra's algorithm. We also compare the LSPD algorithm with the conventional primal-dual algorithm in solving shortest path problems and show their difference due to degeneracy in solving the 1-1 shortest path problems.

A primal-dual method for linear programming problems with fuzzy variables

2010 ◽  
Vol 4 (2) ◽  
pp. 189 ◽  
Author(s):  
A. Ebrahimnejad ◽  
S.H. Nasseri ◽  
F. Hosseinzadeh Lotfi ◽  
M. Soltanifar
Keyword(s):  
Linear Programming ◽  
Dual Method ◽  
Fuzzy Variables ◽  
Primal Dual ◽  
Linear Programming Problems

scholarly journals A primal-dual exterior point algorithm for linear programming problems

2009 ◽  
Vol 19 (1) ◽  
pp. 123-132 ◽  
Author(s):  
Nikolaos Samaras ◽  
Angelo Sifelaras ◽  
Charalampos Triantafyllidis
Keyword(s):  
Linear Programming ◽  
Computational Study ◽  
Optimal Solution ◽  
Simplex Algorithm ◽  
Dual Algorithm ◽  
Optimal Linear ◽  
Primal Dual ◽  
Primal And Dual ◽  
Two Phases ◽  
Feasible Solutions

The aim of this paper is to present a new simplex type algorithm for the Linear Programming Problem. The Primal - Dual method is a Simplex - type pivoting algorithm that generates two paths in order to converge to the optimal solution. The first path is primal feasible while the second one is dual feasible for the original problem. Specifically, we use a three-phase-implementation. The first two phases construct the required primal and dual feasible solutions, using the Primal Simplex algorithm. Finally, in the third phase the Primal - Dual algorithm is applied. Moreover, a computational study has been carried out, using randomly generated sparse optimal linear problems, to compare its computational efficiency with the Primal Simplex algorithm and also with MATLAB's Interior Point Method implementation. The algorithm appears to be very promising since it clearly shows its superiority to the Primal Simplex algorithm as well as its robustness over the IPM algorithm.

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