Duality in Optimization Beyond Convexity
报 告 人：戚厚铎教授
报告时间：2026年8月10日17：00-18：00
报告地点：理学院304
报告人简介：
戚厚铎，香港理工大学教授，深耕运筹优化与最优控制方向。主要研究数学优化、矩阵优化理论，及其在金融建模、机器学习场景下的落地应用。先后于北京大学、曲阜师范大学、中国科学院完成本硕博阶段学习，历任中国科学院、新南威尔士大学博士后研究员，英国南安普顿大学讲师、教授、优化方向讲席教授。先后斩获澳大利亚研究理事会伊丽莎白二世杰出研究员基金、英国艾伦・图灵研究院图灵学者等重磅荣誉，为多家国际权威学术学会会士；长期担任 Asia-Pacific Journal of Operational Research 优化栏目主编，同时兼任 Mathematical Programming Computation、Computational Optimization and Applications、Numerical Functional Analysis and Applications、Journal of Operations Research Society of China等多本国际权威期刊副主编。
报告内容：
Duality has become folklore in optimization. In particular, Fenchel duality has been extensively studied in convex setting. When dealing with nonconvex problems, local duality theory based on Wolfe duality and the augmented Lagrangian has been the theoretical basis for many algorithms. However, they fall short for new applications from modern machine learning applications. For instance, the cardinality optimization has proved to be a general framework for a wide range of applications including image denoising and local duality theory does not extend to it. In this talk, we will introduce a new concept of the stationary duality and its applications to the structural cardinality optimization. We illustrate its basic principle and fundamental properties. We further demonstrate how a proximal point algorithm can be principally developed and its numerical efficiency is verified on image denoising problems. It appears that the Fenchel duality for convex optimization is indispensable in developing a theory and algorithms for stationary duality for cardinality optimization.
