Abstract:

The dynamic stochastic variational inequality (DSVI) is an ordinary differential equation whose right-hand side is defined by the two-stage stochastic variational inequality (SVI). The DSVI provides a unified modelling framework for various applications in which dynamics, uncertainties and equilibrium are present. We show the existence and uniqueness of a solution for two classes of the DSVI in the space of continuously differentiable functions with the space of measurable functions. The first class is defined by a strongly monotone SVI in the second stage, and the second class pertains to a box-constrained P-matrix linear SVI in the second stage. We develop sample average approximation and time-stepping schemes to compute a solution of the DSVI. The uniform convergence and exponential convergence are established for the discrete approximation.  We show applications of the DSVI for optimizing multimodal lager model-based embodied intelligence system for the elderly, where the two-stage SVI arises from stochastic bilevel optimization.  

Biography:

Xiaojun Chen is a Chair Professor of Department of Applied Mathematics, Hong Kong Polytechnic University.  She is the Co-Director of CAS AMSS-PolyU Joint Laboratory of Applied Mathematics.   Her research interests focus on mathematical optimization theory and algorithms for nonsmooth nonconvex optimization problems and stochastic variational inequalities with applications in data sciences. She is the PI of several large grants from Hong Kong Research Grant Council and Croucher Foundation.  She published over 100 papers in top journals in applied mathematics. Currently she is an Associate Editor of SIAM Journal on Optimization and SIAM Journal on Control and Optimization, and the Area Editor of Journal on Optimization Theory and Applications. She is a fellow of Society for Industrial and Applied Mathematics and a fellow of American Mathematical Society. She is a Keynote speaker of the 25th International Symposium on Mathematical Programming in Canada 2024 and a Keynote speaker of the 16th  Viennese Conference on Optimal Control and Dynamic Games in Austria 2025.