2013 Fiscal Year Final Research Report
On robust numerical methods of semidefinite relaxation for polynomial optimization problems
| Project/Area Number |
22560061
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Engineering fundamentals
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2013-03-31
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| Keywords | 最適化 / 錐線形計画 / 多項式計画 / 半正定値計画 |
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| Research Abstract |
We established the theory of facial reduction algorithm (FRA) for conic linear optimization problems, and prove that the conic expansion approach is dual to FRA. For SDP relaxation for polynomial optimization problems (POPs), sometimes we can compute the optimal value of POP by solving the SDP relaxation problem although the SDP problem is infeasible. We elucidated the reason of this phenomena, and proposed a new SDP relaxation scheme using this property.
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