Simplex algorithms

[1]  E. Beale Cycling in the dual simplex algorithm , 1955 .

[2]  T. L. Saaty,et al.  Progress in Operations Research. , 1961 .

[3]  J. Tomlin Modifying Triangular Factors of the Basis in the Simplex Method , 1972 .

[4]  R. Willoughby Sparse matrices and their applications , 1972 .

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

[6]  V. Klee,et al.  HOW GOOD IS THE SIMPLEX ALGORITHM , 1970 .

[7]  George B. Dantzig Inductive Proof of the Simplex Method , 1960, IBM J. Res. Dev..

[8]  George B. Dantzig,et al.  Decomposition Principle for Linear Programs , 1960 .

[9]  L. B. Rall,et al.  Error in Digital Computation , 1965 .

[10]  Shuzhong Zhang,et al.  On anti-cycling pivoting rules for the simplex method , 1991, Oper. Res. Lett..

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

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

[13]  R. Bartels A stabilization of the simplex method , 1971 .

[14]  W. Miranker,et al.  The arithmetic of the digital computer: A new approach , 1986 .

[15]  O. H. Brownlee,et al.  ACTIVITY ANALYSIS OF PRODUCTION AND ALLOCATION , 1952 .

[16]  P. Wolfe A Technique for Resolving Degeneracy in Linear Programming , 1963 .

[17]  Gene H. Golub,et al.  The simplex method of linear programming using LU decomposition , 1969, Commun. ACM.

[18]  John K. Reid,et al.  A sparsity-exploiting variant of the Bartels—Golub decomposition for linear programming bases , 1982, Math. Program..

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

[20]  A. Hoffman On approximate solutions of systems of linear inequalities , 1952 .

[21]  S. M. Robinson Bounds for error in the solution set of a perturbed linear program , 1973 .

[22]  David I. Steinberg,et al.  Letter to the Editor - On the Possibility of Cycling with the Simplex Method , 1978, Oper. Res..

[23]  Eli Hellerman,et al.  Reinversion with the preassigned pivot procedure , 1971, Math. Program..

[24]  Donald Goldfarb,et al.  On the Bartels—Golub decomposition for linear programming bases , 1977, Math. Program..

[25]  Michael A. Saunders,et al.  A FAST, STABLE IMPLEMENTATION OF THE SIMPLEX METHOD USING BARTELS-GOLUB UPDATING , 1976 .

[26]  George B. Dantzig,et al.  Generalized Upper Bounding Techniques , 1967, J. Comput. Syst. Sci..

[27]  J. H. Wilkinson Modern Error Analysis , 1971 .

[28]  H. Markowitz The Elimination form of the Inverse and its Application to Linear Programming , 1957 .

[29]  G. Dantzig,et al.  THE PRODUCT FORM FOR THE INVERSE IN THE SIMPLEX METHOD , 1954 .

[30]  John A. Tomlin,et al.  Updated triangular factors of the basis to maintain sparsity in the product form simplex method , 1972, Math. Program..

[31]  James K. Ho,et al.  An advanced implementation of the Dantzig—Wolfe decomposition algorithm for linear programming , 1981, Math. Program..

[32]  G. Dantzig UPPER BOUNDS, SECONDARY CONSTRAINTS, AND BLOCK TRIANGULARITY IN LINEAR PROGRAMMING , 1955 .

[33]  G. Dantzig,et al.  A Basis Factorization Method for Block Triangular Linear Programs. , 1978 .

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

[35]  G. Stewart,et al.  Sparse Matrix Proceedings. , 1980 .

[36]  J. W. Suurballe,et al.  A note on cycling in the simplex method , 1969 .

[37]  G. Dantzig,et al.  Notes on Linear Programming: Part 1. The Generalized Simplex Method for Minimizing a Linear Form under Linear Inequality Restraints , 1954 .

[38]  R. Bellman,et al.  Proceedings of Symposia in Applied Mathematics. , 1961 .

[39]  H. Crowder,et al.  Partially normalized pivot selection in linear programming , 1975 .