对于单纯形方法来说，小的退化单纯形可能是不好的

Q4 Decision Sciences

Journal of the Operations Research Society of Japan Pub Date : 2017-09-25 DOI:10.15807/JORSJ.60.419

S. Mizuno, Noriyoshi Sukegawa, A. Deza

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引用次数: 0

摘要

我们证明了具有Dantzig枢轴规则的单纯形法可能需要在两个高度退化的实例上进行指数次数的迭代。第一种情况下的可行域是全维单纯形，第二种情况下为单点。此外，约束矩阵、右侧向量和成本向量的条目为{0，1，2}值。这些实例具有较少的顶点和较小的输入数据长度，说明了退化对单纯形方法的影响。

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SMALL DEGENERATE SIMPLICES CAN BE BAD FOR SIMPLEX METHODS

We show that the simplex method with Dantzig’s pivoting rule may require an exponential number of iterations over two highly degenerate instances. The feasible region of the first instance is a full dimensional simplex, and a single point for the second one. In addition, the entries of the constraint matrix, the right-hand-side vector, and the cost vector are {0, 1, 2}-valued. Those instances, with few vertices and small input data length, illustrate the impact of degeneracy on simplex methods.

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来源期刊

Journal of the Operations Research Society of Japan 管理科学-运筹学与管理科学

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： The journal publishes original work and quality reviews in the field of operations research and management science to OR practitioners and researchers in two substantive categories: operations research methods; applications and practices of operations research in industry, public sector, and all areas of science and engineering.