A Class of High-order Copositive Tensor Optimization Problem and Its Applications to Hypergraphs

报告摘要：In this report, we consider a class of copositive optimization problem with high-order copositive tensors, which can be used to estimate the coclique number of uniform hypergraphs. Firstly, we present a checkable equivalent condition for the slater constraint qualification. Then, based on the standard simplex, we focus on solving a new kind of CTOP from hypergraph theory. To do that, two approximation problems are established and a linear approximation algorithm is proposed for the original CTOP. It is proven that the optimal value of the original problem lies between the optimal values of the two approximation problems. Furthermore, relationships between the optimal solutions are considered. Finally, the proposed algorithm is applied to estimate the coclique number of uniform hypergraphs, and numerical results show its efficiency.

报告人简介：陈海滨，曲阜师范大学青年教授，香港理工大学博士（导师：祁力群教授）。国家自然科学基金数理学部通讯评审专家（2020.10--），山东省杰青(2021)，山东省青年创新团队“张量大数据分析与优化”负责人(2021)。

长期从事张量理论、优化及其应用等研究工作，先后申请到国家自然科学基金2项(面上项目1项，青年项目1项)、山东省自然科学基金2项（杰出青年基金1项，青年基金1项）、中国博士后科研基金特别资助项目1项和中国博士后基金面上项目1项。近五年，与祁力群教授合作在Springer出版张量专著《Tensor Eigenvalues and Their Applications》一部，发表SCI论文40多篇，数学ESI 高被引论文4篇。2016年，荣获山东省科学技术奖二等奖。