| 研究課題/領域番号 |
23K16844
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| 研究種目 |
若手研究
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| 配分区分 | 基金 |
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| 審査区分 |
小区分60020:数理情報学関連
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| 研究機関 | 統計数理研究所 |
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研究代表者 |
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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| 研究期間 (年度) |
2023-04-01 – 2028-03-31
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| 研究課題ステータス |
交付 (2023年度)
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| 配分額 *注記 |
4,550千円 (直接経費: 3,500千円、間接経費: 1,050千円)
2027年度: 910千円 (直接経費: 700千円、間接経費: 210千円)
2026年度: 910千円 (直接経費: 700千円、間接経費: 210千円)
2025年度: 910千円 (直接経費: 700千円、間接経費: 210千円)
2024年度: 910千円 (直接経費: 700千円、間接経費: 210千円)
2023年度: 910千円 (直接経費: 700千円、間接経費: 210千円)
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| キーワード | error bounds / log determinant cones / convex cones / power cones / p-cones / continuous optimization / conic optimization / convex analysis |
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| 研究開始時の研究の概要 |
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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| 研究実績の概要 |
(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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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
Two papers were accepted and we completed several preprints on the topics of the project.
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| 今後の研究の推進方策 |
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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