| 研究実績の概要 |
(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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| 次年度使用額が生じた理由 |
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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