| 研究課題/領域番号 |
19K20217
|
|---|
| 研究機関 | 東京大学 |
|---|
研究代表者 |
ロウレンソ ブルノ・フィゲラ 東京大学, 大学院情報理工学系研究科, 助教 (80778720)
|
|---|
| 研究期間 (年度) |
2019-04-01 – 2023-03-31
|
| キーワード | 連続最適化 / 錐最適化 / 恭順錐 / 面縮小法 |
|---|
| 研究実績の概要 |
This project is focused on the analysis and development of robust approaches for conic optimization. During this first year of the project, we worked on laying the theoretical foundations for the project. Our main research achievements for this year are as follows.
(a) The paper "Amenable cones: error bounds without constraint qualifications" that introduces the notion of amenable cones was completed and published at Mathematical Programming. In that paper, a relationship between amenable cones, facial reduction and error bounds is established.
(b) An earlier work on the complete solvability of SDPs using an interior point oracle was extended to all conic linear programs. The main result is that, assuming the capability of solving "well-behaved" problems, we may solve any arbitrary conic linear program through a combination of techniques including the so-called "double facial reduction". This paper is currently under review.
(c) We proved a few more results on the geometry of amenable cones. We will also proved results on convergence rates of several algorithms under general error bounds. Furthermore, error bounds for non-amenable cones are also being explored. These results will be discussed in future papers.
|
| 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
One of the paper was accepted at Mathematical Programming, while another one is at the second round of peer review.
The results on amenable cones were presented in a few conferences in workshops during 2019.
We also have two more papers that are nearing completion and two more that are still in the initial stages.
|
| 今後の研究の推進方策 |
For the next fiscal year, the plan is to continue the analysis of amenable cones and their geometry. This will include analysis of algorithms under error bound conditions that take into account ill-behaved conic programming instances. We will also explore the limits of the class of amenable cones.
Meanwhile, we will continue the writing and development of the papers that were started during the first year.
|
| 次年度使用額が生じた理由 |
A number of conferences and research meetings that were scheduled to happen in February/March were cancelled or rescheduled. Some of those conferences might happen at a later date, so I might need to use to the budget to attend these conferences.
|
