2021 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 | error bounds / exponential cone / p-cones / facial residual function |
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| Outline of Annual Research Achievements |
(a) Completed the preprint "Tight error bounds and facial residual functions for the p-cones and beyond", which is about a new framework for proving tightness of error bound results for conic feasibility problems. This is illustrated with sharp Holderian error bounds for problems involving general p-cones. Surprisingly, those error bounds can be very different from the second-order cone case (i.e., the p=2 case). Some applications are also discussed and, in particular, we use our results to determine the KL exponent of a function related to least squares minimization with p-norm regularization.
(b) Following the results of peer review, some of the papers submitted in the previous fiscal year were revised and now are closer to being accepted. In particular, the framework described in the paper "Error bounds, facial residual functions and applications to the exponential cone" was significantly revised and simplified with more emphasis put on the notion of facial residual functions.
(c) 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
A new preprint was completed. Also, several papers were revised and are now either under "Minor Revision" or "Major Revision".
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| Strategy for Future Research Activity |
(a) Continue the research on error bounds for problems involving other non-symmetric cones such as power cones and hyperbolicity cones.
(b) Continue the research on the facial structure and geometry of convex cones.
(c) Explore the connections between error bounds and convergence rate of algorithms for feasibility problems especially in exotic cases where there are non-Holderian error bounds present.
(d) Present our findings at conferences and workshops.
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| Causes of Carryover |
Amidst the ongoing pandemic, all my travel plans to conferences and workshops were cancelled. Correspondingly, all the travel budget was unused. For the next fiscal year, I am more optimistic that some amount of research travels will be possible, so I plan to use the budget for attending conferences and to visit my collaborators in order to keep active our ongoing projects.
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Research Products
(12 results)
