| 研究課題/領域番号 |
19K20217
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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 (2020-2023)
東京大学 (2019) |
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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) |
2019-04-01 – 2024-03-31
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| 研究課題ステータス |
完了 (2023年度)
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| 配分額 *注記 |
3,120千円 (直接経費: 2,400千円、間接経費: 720千円)
2022年度: 650千円 (直接経費: 500千円、間接経費: 150千円)
2021年度: 910千円 (直接経費: 700千円、間接経費: 210千円)
2020年度: 650千円 (直接経費: 500千円、間接経費: 150千円)
2019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 / amenable cones / facial residual function / nonsymmetric cones / p-cones / hyperbolicity cones / self-duality / automorphism group / exponential cone / 連続最適化 / 錐最適化 / 恭順錐 / 面縮小法 / 錐線形計画問題 / 悪条件問題 / 射影縮尺法 |
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| 研究開始時の研究の概要 |
Conic optimization corresponds to a large class of mathematical problems that have both practical and theoretical relevance. However, sometimes those problems have unfavorable theoretical properties, i.e., they are “ill-posed”. The goal of this project is to analyze mathematical aspects related to ill-posed problems and to research effective methods for solving them.
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| 研究実績の概要 |
(a) We revised two papers related to the project. Finally, they were published at the SIAM Journal on Optimization and Mathematics of Operations Research (MOR), two top journals in the optimization field. These papers continue our study of error bounds of convex cones and include new results on p-cones and power cones. The MOR paper, in particular, presents a framework for proving optimality of the certain types of error bounds we developed in previous works.
(b) Conference presentations. We presented our research findings on error bounds at the SIAM conference on Optimization in Seattle and at the ICIAM conference in Tokyo.
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