2020 Fiscal Year Research-status Report
Solving ill-posed conic optimization problems
| Project/Area Number |
19K20217
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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, 数理・推論研究系, 准教授 (80778720)
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | 連続最適化 / 錐最適化 / 恭順錐 / 面縮小法 |
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| Outline of Annual Research Achievements |
Our main research achievements for this year are as follows:
(a) Two papers were published: "Generalized subdifferentials of spectral functions over Euclidean Jordan algebras" at the SIAM Journal on Optimization and "Solving SDP Completely with an Interior Point Oracle" at the journal Optimization Methods and Software. The former is a work done in the context of Euclidean Jordan Algebras which are intrinsically connected to symmetric cones. We remark that this a class of convex cones we have studied extensively in the course of this project. The latter work is about solving general conic linear programs as thoroughly as possible even in the presence of unfavourable theoretical properties. The techniques described in the paper are illustrated taking as an example the case of semidefinite programming.
(b) We completed two preprints on topics related to the geometry of amenable cones and hyperbolicity cones.
(c) We proved error bounds for the exponential cone and developed an extension of the notion of amenability: g-amenability.
(d) We completed a preprint on the analysis of convergence rates of certain feasibility problems using error bounds.
(e) We presented our results in a few online workshops and conferences.
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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 published and a few preprints were completed/submitted. One of them is currently under at a "Minor Revision".
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| Strategy for Future Research Activity |
We plan to do the following:
(a) Continue to analyze the geometry of amenable cones and associated classes of cones. In particular, we will take a closer look at the so-called "hyperbolicity cones".
(b) Develop more tools to compute error bounds for certain families of cones.
(c) Write (or finish) papers describing our research findings.
(d) Present our results at (online) conferences.
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| Causes of Carryover |
Due to the coronavirus pandemic all conferences/workshops and all travel plans I had were cancelled or were moved to online venues. Therefore, no money was spent on travel.
For the next fiscal year, depending on the pandemic situation, it might be possible to do some limited amount of research travels. If that is not possible, I plan to use the research budget to buy more books or better computer equipment for online meetings and remote collaborative work.
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