北航tyc8722太阳集团学术报告

Tightness of Semidefinite Relaxation and Optimization Landscape of Quadratically Constrained Quadratic Programs

苏文藻（香港中文大学）

报告时间：2026年4月28日星期二  14：30-15：30

报告地点：沙河主楼E803

报告摘要: Quadratically constrained quadratic programs (QCQPs) are ubiquitous in applications and have been extensively studied over the decades. One powerful technique for tackling this important class of optimization problems is semidefinite relaxation (SDR). Although there is a large body of literature on establishing the tightness of SDRs of structured QCQPs, the results therein typically do not yield scalable algorithms for solving those QCQPs. On the other hand, there has been much recent interest in lightweight iterative methods that can directly tackle certain classes of possibly non-convex QCQPs and possess strong convergence guarantees. However, the convergence analyses of most existing methods are conducted on a problem-by-problem basis and do not exploit the fact that the QCQPs in question often have tight SDRs. In this talk, we present conditions under which it is possible to infer the optimization landscape of a QCQP from its tight SDR. This provides a new approach to analyzing the convergence behavior of various iterative methods when applied to the QCQP. We demonstrate the potential of our approach by applying it to various applications in data science.

报告人简介：苏文藻教授现为香港中文大学研究生院院长、晨兴书院代理院长及系统工程与工程管理学系教授，主要研究方向为数学优化理论及其在计算几何、机器学习、信号处理和统计等领域的应用。他于2023年当选IEEE（电机电子工程师学会）会士，2024年当选INFORMS（运筹学与管理学研究协会）高级会员及香港工程师学会会士。他曾获得多个研究和教学奖项，包括2024年INFORMS計算學會獎和《SIAM Review》SIGEST奖、2018年IEEE信号处理分会最佳论文奖、2015年IEEE信号处理分会《IEEE Signal Processing Magazine》最佳论文奖、2014年IEEE通信分会亚太杰出论文奖、2010年INFORMS优化学会青年奖、香港大学教育资助委员会2022年杰出教学奖、香港中文大学2022年博文教学奖、香港中文大学2013年校长模范教学奖等。他的学生也曾获得国内与国外的研究奖项。他现担任数学优化领域国际期刊《Journal of Global Optimization》、《Mathematical Programming》、《Mathematics of Operations Research》、《Open Journal of Mathematical Optimization》和《Optimization Methods and Software》的编辑。他现为中国运筹学会数学规划分会副理事长和常务理事。

邀请人：崔春风