2023 Fiscal Year Research-status Report
Towards new classes of conic optimization problems
| Project/Area Number |
23K16844
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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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| Keywords | error bounds / log determinant cones / convex cones / power cones / p-cones |
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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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| Causes of Carryover |
Due to some unforeseen circumstances, I had to cancel some of the research travel plans I had. This next fiscal year, however, I am planning to use part of the budget to attend some conferences and workshops.
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