报告题目：Is it possible that all polynomial optimization problems are equivalent with convex formulations?

报 告 人：陈海滨 教授 （曲阜师范大学）

报告时间：2023/3/21 (周二)下午3：00-4：00

报告地点：腾讯会议ID：610-519-378

报告校内联系人：郭 峰 副教授     联系电话：84708351-8088

报告摘要：Polynomial optimization includes a very rich class of problems in which both the objective and constraints can be written in terms of polynomials on the decision variables. Recently, polynomial optimization problems have been formulated as a relaxed conic program over a convex set. In this report, we study equivalent convex reformulations for general polynomial optimization problems. By the definition of recession cone, we prove that all feasible polynomial optimization problems are equivalent to convex optimization problems with linear objective functions. The reformulated convex optimization problem is a conic problem with tensor variables

defined in the sum of two convex sets. Particularly, we show that polynomial optimization problems with linear constraints are equivalent with completely positive programs which are linear programs with completely positive tensor variables. Furthermore, the equivalent copositive optimization problems are given for the case with linear constraints, which are dual problems of the obtained completely positive optimization problems. It is shown that the strong duality holds under some conditions.

报告人简介：陈海滨，教授，国家自然科学基金通讯评审专家，山东省杰青，中国高等教育学会教育数学专委会理事，山东省高校青年创新团队发展计划带头人。主要从事张量大数据分析与优化、非线性最优化理论算法及应用、图像处理等方面的工作。先后主持国家自然科学基金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，青年项目1项）、中国博士后科研基金特别资助1项和中国博士后基金面上项目1项。与祁力群教授在Springer出版社出版张量专著1部；发表SCI论文50多篇，ESI高被引论文4篇。曾获2015-2016年度香港理工大学SIAM Chapter年度杰出贡献奖；2016年，山东省高等学校科学技术奖二等奖（自然科学类）。