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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) 我们完成了关于以下主题的几份预印本：双曲锥体的几何形状、功率锥体的误差界限和多面体锥体的自对偶性。在我们的结果中，我们能够证明所有双曲锥都是合适的，并且我们还在某些条件下研究了它们的自同构群。对于功率锥，我们完全确定了它们的误差界限和自同构。最后，我们证明了多面体锥体的自对偶性可以通过其松弛矩阵之一的正半定性完全检测到，并且我们证明了不可约自对偶多面体锥体的松弛矩阵与双非负矩阵的极端射线之间存在令人惊讶的联系。（b）在对上一财年进行同行评审的论文进行修改之后，其中几篇论文最终被接受优化及邻近领域的重要期刊。这包括《SIAM 优化杂志》、《SIAM 应用代数和几何杂志》、《SIAM 矩阵分析杂志》、《数学规划》和《计算数学基础》上的论文。(c) 我们在在线和现场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。