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A Basis-Deficiency-Allowing Variation of the Simplex Method for Linear Programming
h one of the most important and fundamental concepts in the simplex methodology, basis is restricted to being a square matrix of the order exactly equal to the number of rows of the coefficientExpand
A Basis-Deficiency-Allowing Variation of the Simplex Method for Linear Programming
h one of the most important and fundamental concepts in the simplex methodology, basis is restricted to being a square matrix of the order exactly equal to the number of rows of the coefficientExpand
A phase-1 approach for the generalized simplex algorithm
Abstract A new simplex variant allowing basis deficiency has recently been proposed to attack the degeneracy [1]. As a generalization of the simplex algorithm, it uses a Phase-1 procedure, solving anExpand
Practical finite pivoting rules for the simplex method
ZusammenfassungPivot-Regeln sind ein wesentliches Element der Simplexmethode. In dieser Arbeit stellen wir zwei Varianten von Pivot-Regeln des „Bland'schen Typs“ vor. Während die Bland-Regel aufExpand
A dual projective simplex method for linear programming
The method proposed in this paper is a dual version of the projective simplex method, developed by the author. Providing a stable alternative setting for the dual simplex method, by handling aExpand
Linear Programming Computation
Introduction.- Geometry of the Feasible Region.- Simplex Method.- Duality principle and dual simplex method.- Implementation of the Simplex Method.- Sensitivity Analysis and Parametric LP.- VariantsExpand
Efficient nested pricing in the simplex algorithm
  • Pingqi Pan
  • Mathematics, Computer Science
  • Oper. Res. Lett.
  • 1 May 2008
We report a remarkable success of nested pricing rules over major pivot rules commonly used in practice, such as Dantzig's original rule as well as the steepest-edge rule and Devex rule.
A primal deficient-basis simplex algorithm for linear programming
  • Pingqi Pan
  • Mathematics, Computer Science
  • Appl. Math. Comput.
  • 1 March 2008
TLDR
A primal simplex algorithm using sparse LU factors of deficient bases that significantly outperformed MINOS 5.3 in terms of both iteration counts and run time and reveals that there is no inevitable correlation between an algorithm’s inefficiency and degeneracy. Expand
The most-obtuse-angle row pivot rule for achieving dual feasibility: A computational study
We recently proposed several new pivot rules for achieving dual feasibility in linear programming, which are distinct from existing ones: the objective function value will no longer changeExpand
A Revised Dual Projective Pivot Algorithm for Linear Programming
  • Pingqi Pan
  • Mathematics, Computer Science
  • SIAM J. Optim.
  • 1 May 2005
TLDR
This work revise the dual projective pivot algorithm using sparse rectangular LU factors and uses a so-called pseudobasis (a rectangular matrix having fewer columns than rows), thereby solving smaller linear systems with a potentially improved stability compared to simplex algorithms. Expand
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