The Klee-Minty problem is a linear-programming problem designed to demonstrate that a problem exists that would require the simplex algorithm to generate all extreme point solutions before finding the optimal. This problem demonstrated that, although the simplex algorithm (under a nondegeneracy assumption) would find an optimal solution in a finite number of iterations, the number of iterations can increase exponentially. Thus, the simplex method is not a polynomially bounded algorithm. One form of the Klee-Minty problem, which defines a slightly perturbed hypercube, is the following:
with 0 < ∈ < 1/2.
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© 2001 Kluwer Academic Publishers
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Gass, S.I., Harris, C.M. (2001). Klee-minty problem . In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_499
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DOI: https://doi.org/10.1007/1-4020-0611-X_499
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