| Project/Area Number |
23K16844
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 60020:Mathematical informatics-related
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
ロウレンソ ブルノ・フィゲラ 統計数理研究所, 統計基盤数理研究系, 准教授 (80778720)
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| Project Period (FY) |
2023-04-01 – 2028-03-31
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| Project Status |
Granted (Fiscal Year 2023)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2027: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2026: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2025: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2024: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2023: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | error bounds / log determinant cones / convex cones / power cones / p-cones / continuous optimization / conic optimization / convex analysis |
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| Outline of Research at the Start |
In this project we aim to investigate conic optimization problems over general cones,
with a focus on problems beyond semidefinite programming. This will include the study of
theoretical properties and the development of reliable algorithms.
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| Outline of Annual Research Achievements |
(a) We completed several new preprints on topics related to this project. This includes a paper on error bounds for log determinant cones; a preprint on the geometry of copositive cones over symmetric cones; a new framework for eigenvalue programming and, finally, a study on closing duality gaps of semidefinite programs via a perturbation approach.
(b) We also had papers accepted on error bounds of p-cones and power cones. They will be published at the Mathematics of Operations Research and at the SIAM Journal on Optimization.
(c) We had in-person research meetings with overseas collaborators where we explored some themes related to this project.
(d) We presented our results at the SIAM conference on Optimization in Seattle and at the ICIAM conference in Tokyo.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
Two papers were accepted and we completed several preprints on the topics of the project.
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| Strategy for Future Research Activity |
We will continue exploring new classes of convex cones and their geometry. This will include, in particular, a focus on new results for homogeneous cones, hyperbolicity cones and an exploration of the facial exposedness properties of certain convex cones. Whenever possible, we will also try to get appropriate error bound results and connect them to convergence properties of certain algorithms.
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