2013 Fiscal Year Final Research Report
Development of highly accurate algorithms for semidefinite programming problems
| Project/Area Number |
22740056
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Kyushu University (2012-2013)
The University of Electro-Communications (2010-2011) |
|---|
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)
|
|---|
| Project Period (FY) |
2010-04-01 – 2014-03-31
|
| 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 |
|---|
| 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.
|
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
[Remarks] 脇 隼人, 最適化手法の全体像, 2013年度プラントモデリング部会, 富士通研究所, 2013年7月(アウトリーチ活動)
