Linear programming: methods and applications (5th ed.)
Linear programming: methods and applications (5th ed.)
Classroom Note: Hoffman's Circle Untangled
SIAM Review
Exact arithmetic at low cost—a case study in linear programming
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Finite Algorithms in Optimization and Data Analysis
Finite Algorithms in Optimization and Data Analysis
Cycling in linear programming problems
Computers and Operations Research
Operations Research Letters
Short communication: A note on cycling LP examples with permutation structure
Computers and Operations Research
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We answer two questions that naturally arise while dealing with Hoffman's celebrated 50-year-old linear program to be solved by the primal simplex method, where an angle @q and a scaling factor @w are adjustable parameters. In particular, we determine what conditions have to be imposed on @w for classical cycling to occur with @q=2@p/5, and what on @q with @w=+/-tan(@q). The first answer reveals that the sufficient condition widely spread over the literature is false, so fixing it turns this example into a correct example of classical cycling. Some progress towards necessary and sufficient conditions for cycling to occur in this example is also reported.