题    目：Optimal Spectral Design with Prior Information

嘉　宾：Weijun Xie 教授，香港城市大学

主持人：曾智宇 助理教授 上海交通大学安泰经济与管理学院

时　间：2026年10月14日（周三）14:00-15:30

地　点：上海交通大学安泰经济与管理学院包兆龙图书馆A507

内容简介：

We study a class of spectral design problems in which a prior positive semidefinite information matrix is updated by a sum of rank-one matrices constructed from chosen design vectors subject to a bound on their Euclidean norm. The objective of a spectral design problem is any symmetric convex function of the eigenvalues of the updated information matrix. This framework unifies classical optimal experimental design criteria, including A-, D-, and E-optimality. It also arises in model-based derivative-free optimization, where sampling directions determine the conditioning and accuracy of regression models. Although the objective is symmetric and convex in the eigenvalues, the optimization problem with design vectors/matrix as decision variables is nonconvex, and optimal solutions of their convex relaxations may not be feasible for the spectral design problem. We use tight eigenvalue relaxations to obtain a convex reformulation, and we apply the Schur–Horn theorem to construct a simple polynomial-time algorithm for solving the spectral design problem. We illustrate the optimal spectral designs computed by our algorithm. Moreover, a small set of numerical experiments shows the potential of spectral designs for derivative-free optimization.

演讲人简介：

Dr. Weijun Xie is a Professor in the Department of Data Science at City University of Hong Kong. His research interests are theory and applications of stochastic, discrete, and convex optimization. His work has received multiple awards, including the 2025 INFORMS Computing Prize (Honorable Mention), the 2022 New Investigator Award from the Virginia Space Grant Consortium (NASA), the 2021 NSF CAREER Award, and the 2020 INFORMS Young Researchers Paper Prize. He currently serves as Associate Editor of Operations Research, Mathematical Programming, Manufacturing & Service Operations Management, Journal of Global Optimization, and Naval Research Logistics.

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