2016 Fiscal Year Final Research Report
Studies on Diameter of High-Dimensional Polyhedra and Complexity of Simplex Method
Project/Area Number |
15H06617
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Research Category |
Grant-in-Aid for Research Activity Start-up
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Allocation Type | Single-year Grants |
Research Field |
Mathematical informatics
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Research Institution | Chuo University |
Principal Investigator |
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Project Period (FY) |
2015-08-28 – 2017-03-31
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Keywords | 多面体理論 / 単体法 / 計算量 |
Outline of Final Research Achievements |
In this research, we investigate the diameter of polyhedra. In particular, we improved the current best upper bound on the diameter of a polyhedron in terms of two parameters: dimension and number of facets of the given polyhedron. Finding a good upper bound on the diameter of a polyhedron is an outstanding open problem in the area of polyhedral combinatorics. We devised (i) a computer-assisted proof method for deriving numerically improved upper bounds and (ii) new proof techniques for deriving theoretically improved upper bounds especially for high-dimensional polyhedra.
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Free Research Field |
オペレーションズ・リサーチ,特に,最適化の理論と応用
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