Efficient nested pricing in the simplex algorithm

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.

[1]  Michel Bénichou,et al.  The efficient solution of large-scale linear programming problems—some algorithmic techniques and computational results , 1977, Math. Program..

[2]  Ping-Qi Pan,et al.  A projective simplex method for linear programming , 1999 .

[3]  Yuval Rabani,et al.  Linear Programming , 2007, Handbook of Approximation Algorithms and Metaheuristics.

[4]  G. M. Clemence,et al.  Blow up of smooth solutions to the barotropic compressible magnetohydrodynamic equations with finite mass and energy , 2008, 0811.4359.

[5]  Robert G. Bland,et al.  New Finite Pivoting Rules for the Simplex Method , 1977, Math. Oper. Res..

[6]  T. Koopmans,et al.  Activity Analysis of Production and Allocation. , 1952 .

[7]  A. Charnes Optimality and Degeneracy in Linear Programming , 1952 .

[8]  Ping-Qi Pan,et al.  A largest-distance pivot rule for the simplex algorithm , 2008, Eur. J. Oper. Res..

[9]  T. Terlaky A convergent criss-cross method , 1985 .

[10]  Donald Goldfarb,et al.  A practicable steepest-edge simplex algorithm , 1977, Math. Program..

[11]  P.-Q Pan A Basis-Deficiency-Allowing Variation of the Simplex Method for Linear Programming , 2003 .

[12]  Nesa L'abbe Wu,et al.  Linear programming and extensions , 1981 .

[13]  Pingqi Pan,et al.  Practical finite pivoting rules for the simplex method , 1990 .

[14]  Shuzhong Zhang,et al.  Pivot rules for linear programming: A survey on recent theoretical developments , 1993, Ann. Oper. Res..

[15]  Ping-Qi Pan,et al.  A projective simplex algorithm using LU decomposition , 2000 .

[16]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[17]  Pingqi Pan A Basis-Deficiency-Allowing Variation of the Simplex Method for Linear Programming , 1998 .

[18]  Robert E. Bixby,et al.  Solving Real-World Linear Programs: A Decade and More of Progress , 2002, Oper. Res..

[19]  Donald Goldfarb,et al.  Steepest-edge simplex algorithms for linear programming , 1992, Math. Program..

[20]  I. Maros Computational Techniques of the Simplex Method , 2002 .

[21]  Paula M. J. Harris Pivot selection methods of the Devex LP code , 1973, Math. Program..

[23]  William Orchard-Hays,et al.  Advanced Linear-Programming Computing Techniques , 1968 .