Klee-minty problem
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First Online:
DOI: https://doi.org/10.1007/1-4020-0611-X_499
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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:
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© Kluwer Academic Publishers 2001