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Solving ill-posed conic optimization problems

解决不适定圆锥优化问题

基本信息

批准号：
19K20217
负责人：
ロウレンソブルノ・フィゲラ
金额：
$ 2万
依托单位：
The Institute of Statistical Mathematics (2020-2022)The University of Tokyo (2019)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Early-Career Scientists
财政年份：
2019
资助国家：
日本
起止时间：
2019-04-01 至 2024-03-31
项目状态：
已结题

项目摘要

(a) We completed several preprints on the following topics: geometry of hyperbolicity cones, error bounds for power cones and self-duality of polyhedral cones. Among our results, we were able to show that all hyperbolicity cones are amenable and we also investigated their automorphism group under certain conditions. For power cones, we completely determined their error bounds and automorphisms. Finally, we showed that self-duality for a polyhedral cone can be completely detected through the positive semidefiniteness of one of its slack matrices and we showed a surprising connection between slack matrices of irreducible self-dual polyhedral cones and extreme rays of doubly nonnegative matrices.(b) Following the revision of papers that were in peer-review in the previous fiscal year, several of those papers were finally accepted at important journals in optimization and neighbouring areas. This includes papers in SIAM Journal on Optimization, SIAM Journal on Applied Algebra and Geometry, SIAM Journal on Matrix Analysis, Mathematical Programming and Foundations of Computational Mathematics.(c) We presented our results in workshops and conferences both online and in-person. There were also research visits to collaborators in Australia and Brazil.

(a)完成了双曲锥的几何、幂锥的误差界和多面体锥的自对偶等几个主题的预印本。在我们的研究结果中，我们证明了所有双曲锥都是可服从的，并在一定条件下研究了它们的自同构群。对于幂锥，我们完全确定了它们的误差界和自同构。最后，我们证明了一个多面体锥的自对偶性可以通过它的一个松弛矩阵的正半定性来完全检测，并证明了不可约的自对偶多面体锥的松弛矩阵与双重非负矩阵的极值射线之间的惊人联系。(b)在对上一财政年度同行评议的论文进行修订后，其中几篇论文终于在最优化和邻近领域的重要期刊上被接受。这包括SIAM杂志上的论文优化，SIAM杂志上的应用代数和几何，SIAM杂志上的矩阵分析，数学规划和计算数学基础。(c)我们在网上和面对面的研讨会和会议上展示了我们的成果。还对澳大利亚和巴西的合作者进行了研究访问。