Survey of solved and open problems in the degeneracy phenomenon
Mathematical Programming: Series A and B - Mathematical Models and Their Solutions
A simplex algorithm for piecewise-linear programming 11: finiteness, feasibility and degeneracy
Mathematical Programming: Series A and B
Parametric linear programming and anti-cycling pivoting rules
Mathematical Programming: Series A and B
A practical anti-cycling procedure for linearly constrained optimization
Mathematical Programming: Series A and B
Classroom Note: Hoffman's Circle Untangled
SIAM Review
Degeneracy subgraph of the Lemke complementary pivot algorithm and anticycling rule
Journal of Optimization Theory and Applications
An Integral Simplex Algorithm for Solving Combinatorial Optimization Problems
Computational Optimization and Applications
Cycling in linear programming problems
Computers and Operations Research
Mathematical Programming: Series A and B
Resolution of the problem of degeneracy in a primal and dual simplex algorithm
Operations Research Letters
Short communication: A note on cycling LP examples with permutation structure
Computers and Operations Research
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We present systematic procedures to construct examples of linear programs that cycle when the simplex method is applied. Cycling examples are constructed for diverse variants of pivot selection strategies: most negative reduced-cost and steepest-edge rule for the entering variable, and smallest ratio rule for the leaving variable (where ties are broken according to the least-index or the largest coefficient criterion, respectively). The results are of theoretical interest since only a limited number of cycling examples have been presented in the literature up to date. Constructed cycling examples may also serve as test problems to evaluate the practical performance of anticycling procedures or new variants of simplex type methods.