Visualizing and Constructing Cycles in the Simplex Method

References

• Balinski M., Tucker A. Duality theory of linear programs—A constructive approach with applications. SIAM Rev. (1969) 11(3):347–377Crossref, Google Scholar
• Beale E. Cycling in the dual simplex method. Naval Res. Logist. Quart. (1955) 2(4):269–275Crossref, Google Scholar
• Chvátal V.Linear Programming (1983) (Freeman, New York) Google Scholar
• Dantzig G.Linear Programming and Extensions (1963) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Fukuda K., Lüthi H.-J. Optimization techniques. (1999) . Course notes, Institute for Operations Research, ETHZ. Zurich, SwitzerlandGoogle Scholar
• Gass S.Linear Programming: Methods and Applications (1964) 2nd ed.(McGraw-Hill Book Company, New York) Google Scholar
• Gass S., Vinjamuri S. Erratum to “Cycling in linear programming problems” (Comput. Oper. Res. 2004 31(2) 303–311). Comput. Oper. Res. (2006) 33(8):2445Crossref, Google Scholar
• Guerrero-García P., Santos-Palomo Á. On Hoffman's celebrated cycling LP example. Comput. Oper. Res. (2007) 34(9):2709–2717Crossref, Google Scholar
• Hall J., McKinnon K. The simplest examples where the simplex method cycles and conditions where EXPAND fails to prevent cycling. Math. Programming (2004) 100(1):133–150Crossref, Google Scholar
• Hoffman A.Cycling in the Simplex Algorithm (1953) (National Bureau of Standards, Washington, D.C.) Google Scholar
• Kaluzny B. Linear programming: Pivoting on polyhedra and arrangements. (2006) . Ph.D. dissertation, School of Computer Science, McGill University, Montreal, Quebec, CanadaGoogle Scholar
• Lee J. Hoffman's circle untangled. SIAM Rev. (1997) 39:98–105Crossref, Google Scholar
• Marshall K., Suurballe J. A note on cycling in the simplex method. Naval Res. Logist. Quart. (1969) 16(1):121–137Crossref, Google Scholar
• Nering E., Tucker A.Linear Programs and Related Problems (1993) (Academic Press, Boston) Google Scholar
• Sierksma G.Linear and Integer Programming (1996) 2nd ed.(Marcel Dekker Inc., New York) Google Scholar
• Solow D.Linear Programming: An Introduction to Finite Improvement Algorithms (1984) (North-Holland Press, Amsterdam, The Netherlands) Google Scholar
• Yudin D., Gol'shtein E.Linear Programming (1965) (Israel Program of Scientific Translations, Jerusalem, Israel) Google Scholar
• Zhang S. New variants of finite criss-cross algorithms for linear programming. Eur. J. Oper. Res. (1999) 116:607–614Crossref, Google Scholar
• Zörnig P. Systematic construction of examples for cycling in the simplex method. Comput. Oper. Res. (2006) 33(8):2247–2262Crossref, Google Scholar