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A Basis-Deficiency-Allowing Variation of the Simplex Method for Linear Programming

- Pingqi Pan
- 2003

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 coefficient… Expand

A Basis-Deficiency-Allowing Variation of the Simplex Method for Linear Programming

- Pingqi Pan
- Mathematics
- 1 August 1998

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 coefficient… Expand

A phase-1 approach for the generalized simplex algorithm

- Pingqi Pan, Yunpeng Pan
- Mathematics
- 1 November 2001

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 an… Expand

Practical finite pivoting rules for the simplex method

- Pingqi Pan
- Mathematics
- 1 December 1990

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 auf… Expand

A dual projective simplex method for linear programming

- Pingqi Pan
- Mathematics
- 1 March 1998

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 a… Expand

Linear Programming Computation

- Pingqi Pan
- Mathematics
- 28 March 2014

Introduction.- Geometry of the Feasible Region.- Simplex Method.- Duality principle and dual simplex method.- Implementation of the Simplex Method.- Sensitivity Analysis and Parametric LP.- Variants… Expand

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

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The most-obtuse-angle row pivot rule for achieving dual feasibility: A computational study

- Pingqi Pan
- Mathematics
- 16 August 1997

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 change… Expand

A Revised Dual Projective Pivot Algorithm for Linear Programming

- Pingqi Pan
- Mathematics, Computer Science
- SIAM J. Optim.
- 1 May 2005

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