Exploration of Conic Linear Programs and Development of Mathematical Modeling
| Project/Area Number |
15H02968
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Social systems engineering/Safety system
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| Research Institution | National Graduate Institute for Policy Studies |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
北原 知就 東京工業大学, 工学院, 助教 (10551260)
速水 謙 国立情報学研究所, 情報学プリンシプル研究系, 教授 (20251358)
上野 玄太 統計数理研究所, モデリング研究系, 教授 (40370093)
小原 敦美 福井大学, 学術研究院工学系部門, 教授 (90221168)
ロウレンソ ブルノ・フィゲラ 成蹊大学, 理工学部, 助教 (80778720)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥15,210,000 (Direct Cost: ¥11,700,000、Indirect Cost: ¥3,510,000)
Fiscal Year 2017: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2016: ¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
Fiscal Year 2015: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
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| Keywords | 線形計画問題 / 半正定値計画問題 / 2次錐計画問題 / 面縮小法 / 悪条件性 / モデリング / Chubanov / 凸最適化 / 線形計画法 / 半正定値計画法 / 対称錐計画法 / 2次錐計画法 / グラフィカルモデル / 行列エントロピー / 共役勾配法 |
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| Outline of Final Research Achievements |
In this research, we studied modeling, mathematics and algorithm of conic linear programs. We developed a new facial reduction algorithm which takes advantage of polyhedral structure when the cone associated with the problem is written as the direct product of nonlinear cones and polyhedral cones, and demonstrated that for an important case of DNN cone, it reduces computational complexity dramatically. We also developed a few new algorithms for conic linear programs including an extension of Chubanov's new polynomial-time linear programming algorithm to symmetric cone programming including SDP and SOCP. We succeeded in development of new implementation of interior-point algorithms for linear programming which only employees Krylov subspace iterative methods for solving the system of linear equations arises in computing search directions. We claim that the implementation for the first time succeeded in solving extensive number of Netlib instances just by using the iterative solvers.
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| Academic Significance and Societal Importance of the Research Achievements |
線形計画問題は最適化の中心的問題として多くの分野で広く活用されてきた．近年その拡張として，凸錐上の線形計画問題，特に半正定値計画問題と２次錐計画問題が注目されている．これらの問題は，線形計画の変数の非負制約を，変数が半正定値対称行列錐や２次錐の直積などに属する，という条件に置き換えたもので，内点法による求解が可能となり，新たなモデリングの道具として期待されている．しかしながらそれらを自在に活用するためには問題の悪条件性, 解法の安定性，モデリング技術など，種々の問題を解決する必要がある．本研究は，凸錐上の線形計画法の技術を古典的線形計画法のレベルに引き上げる上で，着実な一歩を進めたものである．
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Report
(4 results)
Research Products
(15 results)
