Methods and applications for nonlinear second-order cone and semidefinite programming problems
Project/Area Number |
26730012
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Mathematical informatics
|
Research Institution | Kyoto University |
Principal Investigator |
Fukuda Hidemi 京都大学, 情報学研究科, 助教 (40726361)
|
Research Collaborator |
FUKUSHIMA Masao
YAMASHITA Nobuo
LOURENCO Bruno F.
HU Ming
|
Project Period (FY) |
2014-04-01 – 2018-03-31
|
Project Status |
Completed (Fiscal Year 2017)
|
Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
Keywords | 非線形2次錐計画問題 / 非線形半正定値計画問題 / 錐計画問題 / 2乗スラック変数 / ペナルティ法 / 錐最適化問題 / 半正定値計画問題 / 2乗スラック変数 / 正確な拡張ラグランジュ法 / 多目的最適化問題 / 2次錐計画問題 / 2次錐計画問題 / スラック変数 |
Outline of Final Research Achievements |
In this project, we considered methods for conic optimization problems,in particular,nonlinear programming (NLP), nonlinear second-order cone programming (SOCP), and nonlinear semidefinite programming (SDP). We first focused in two methods: differentiable exact penalty functions, and squared slack variables techniques.For both methods, the theoretical analysis,implementations and numerical experiments were successfully done using NLP, SOCP and SDP. For the slack variables technique, we also obtained results for more general symmetric conic problems.We further proposed a method called exact augmented Lagrangian for SOCP and SDP, which has some similarities with the exact penalty method.Moreover, we proposed a new DC method for general conic optimization problems. All the methods proposed and analyzed so far replace difficult conic problems with easier problems, that are well-understood by the community. Related to these, we also studied some methods for multiobjective problems.
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Report
(5 results)
Research Products
(29 results)