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Klee–Minty cube : ウィキペディア英語版
Klee–Minty cube

The Klee–Minty cube (named after Victor Klee and George J. Minty) is a unit cube whose corners have been slightly perturbed. Klee and Minty demonstrated that Dantzig's simplex algorithm has poor worst-case performance when initialized at one corner of their "squashed cube".
In particular, many optimization algorithms for linear optimization exhibit poor performance when applied to the Klee–Minty cube. In 1973 Klee and Minty showed that Dantzig's simplex algorithm was not a polynomial-time algorithm when applied to their cube. Later, modifications of the Klee–Minty cube have shown poor behavior both for other basis-exchange pivoting algorithms and also for interior-point algorithms.
==Description of the cube==

The Klee–Minty cube was originally specified with a parameterized system of linear inequalities, with the dimension as the parameter. When the dimension is two, the "cube" is a squashed square. When the dimension is three, the "cube" is a squashed cube. Illustrations of the "cube" have appeared besides algebraic descriptions.〔〔

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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