2017 Fiscal Year Final Research Report
Conic Programming: Degeneracy and Modeling
| Project/Area Number |
26330025
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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 | The University of Electro-Communications |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
土谷 隆 政策研究大学院大学, 政策研究科, 教授 (00188575)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 錐線形計画 / 半正定値計画 / ２次錐計画 / モデリング / 多項式計画 |
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| Outline of Final Research Achievements |
It is known that the semidefinite programming (SDP) relaxation method for polynomial optimization problems (POPs) can sometimes find the optimal value of POP although the true optimal value of SDP is different from the value. We gave a theoretical explanation for the mysterious phenomenon. This result is exactly to accomplish (part of) the original research objective. In addition, we gave new theoretical findings on degeneracy such as weak infeasibility in second-order programming problems and SDPs. In particular, we propose a new decomposition method for conic feasibility problems, and succeeded in shrinking the feasibility problem into smaller problems.
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| Free Research Field |
数値的最適化
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