Development of highly accurate algorithms for semidefinite programming problems
| Project/Area Number |
22740056
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyushu University (2012-2013)
The University of Electro-Communications (2010-2011) |
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Principal Investigator |
WAKI Hayato 九州大学, マス・フォア・インダストリ研究所, 准教授 (00567597)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 半正定値計画 / 面的縮小 / 多項式最適化問題 / 半正定値計画緩和 / 高精度計算 / 対称錐上の線形最適化問題 / 面的縮小法 / 半正定値計画問題 / H∞制御問題 / 線形行列不等式 / 低ランク解 / 国際情報交換 / 凸集合 / 数理計画法 |
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| Research Abstract |
We mainly proposed an algorithm to remove ill-conditionedness in a given semidefinite programming problems (SDPs). In particular, we focus on ill-conditioned SDP, i.e., the SDP or its dual do not have any interior feasible solutions. Our results are: (1) We proposed a pre-processor for ill-conditioned SDP. It generates an equivalent and well-conditioned SDP with the original. Furthermore, we proposed a similar pre-processor for conic optimization problems, (2) We traced a reason why the resulting SDP from some applications are ill-conditioned, (3) We proposed an algorithm to generate well-conditioned SDP for polynomial optimization problems.
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Report
(5 results)
Research Products
(48 results)
