2017 Fiscal Year Final Research Report
Is the simplex method a polynomial algorithm? --Steps to the unsolved problem--
| Project/Area Number |
15K15941
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical informatics
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
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| Research Collaborator |
MIZUNO Shinji (90174036)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | 単体法 / 線形計画問題 / 多項式アルゴリズム |
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| Outline of Final Research Achievements |
The main results of this research program are as follows (They are all done through joint works). (a) We analyzed the steepest-edge rule for the simplex method, which is one of practical pivot rules. As result, We proved a theoretical upper bound for the rule for the first time. (b) We proposed a new variant of LP-Newton method. For the variant, the bisection method is incorporated. I analyzed the proposed method and obtained theoretical implications for the number of iterations of the variant. (c) We were able to extend Chubanov's algorithm, a new polynomial algorithm for linear programming problems, to more general, second order cone programming problems and symmetric cone programming problems. (d) We developed an approximation algorithm for a class of integer programming problems.
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| Free Research Field |
数理計画法
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