题目：带参数优化的微分随机变分不等式

演讲人：陈小君教授，香港理工大学应用数学系

主持人：林贵华教授，上海大学管理学院

时间：2026年1月7日（周三），上午10:00

地点：上海大学校本部东区1号楼管理学院420会议室

主办单位：上海大学管理学院、上海大学管理学院青年教师联谊会

演讲人简介：

国际知名优化专家，香港理工大学应用数学系讲席教授，美国工业与应用数学学会会士、美国数学学会会士，2026年国际数学家大会45分钟报告人。曾任香港理工大学应用数学系主任和大数据分析中心实验室主任。研究方向包括非光滑非凸优化问题和随机变分不等式的数学优化理论与算法及其在数据科学中的应用，发表论文100余篇。现任/曾任SIAM Journal on Numerical Analysis、SIAM Journal on Optimization、SIAM Journal on Control and Optimization等多个国际著名杂志的副主编。

演讲内容简介：

Variational inequality provides a broad unifying setting for equilibrium problems and optimization. Differential variational inequality and stochastic variational inequality are its generalizations and promising modelling paradigms when dynamics and uncertainties are involved in data analysis and decision making. We first discuss the mathematical formulations and recent results of the differential VI and stochastic VI. Next we introduce the differential stochastic VI with parametric optimization (DSVIO), an ordinary differential equation whose right-hand side is defined by a stochastic VI and solutions of several stochastic optimization problems. The DSVIO provides a powerful modelling framework for various applications in data science and artificial intelligence. We provide sufficient conditions for the existence of a solution pair for the DSVIO in the space of absolutely continuous functions and the space of measurable functions. We discuss a convergent sample average approximation and time-stepping discretization scheme for numerical solutions of the DSVIO. Finally, we show applications of the DSVIO for optimizing multimodal large model-based embodied intelligence systems for the elderly mobility.

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