Development of algorithms for solving conic complementarity problems and semi-infinite programming problems, and their applications to transportation planning problems
| Project/Area Number |
26330022
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical informatics
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| Research Institution | Tohoku University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 最適化 / 均衡問題 / 交通計画 / アルゴリズム / 情報基礎 / 国際情報交換（台湾） |
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| Outline of Final Research Achievements |
The initial purpose of this research was to develop efficient algorithms for solving conic complementarity problems and semi-infinite programming problems, and to apply them to real problems in transportation planning. For the algorithm aspects, we have developed explicit exchange algorithm for convex semi-infinite programming problems with second-order cone constraints, and simplex-based algorithms for solving second-order cone programming problems via semi-infinite programming transformation. For the application aspects, we have analyzed the departure time choice equilibrium problems with multi-bottlenecks network and developed the models for evaluating the optimal placement of rockfall protection structures on a road.
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| Academic Significance and Societal Importance of the Research Achievements |
錐相補性問題や半無限計画問題といった問題に関する研究は主に数理工学系の研究者によって行われているため，実問題への応用が二の次となりがちであった．一方，交通計画学は土木工学の一分野として発展してきた歴史もあり，数理最適化の技法の活用が十分とは言えない側面があった．本研究では，特殊なクラスの最適化問題に対するアルゴリズム開発とその収束解析に関していくつか成果が得られたが，それだけでなく，交通計画や落石対策工設置問題といった現実問題に対する成果も得られた．現実世界を対象とする土木工学と，数理最適化の分野の橋渡しをするという意味でも，本課題で得られた研究成果は意義深いものであるといえる．
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Report
(6 results)
Research Products
(31 results)
