勷勤数学•领军学者报告

题      目：Dynamic Stochastic Bilevel Optimization and Variational Inequalities

报  告  人：Xiaojun Chen 教授  (邀请人：黎稳)

                                             The Hong Kong Polytechnic University       

时      间：4月16日  10：30-11：30

地     点：数科院东楼阶梯二楼报告厅

报告人简介:

        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 90 papers in top journals in applied mathematics. She is an Associate Editor of  SIAM J. Optimization, SIAM J. Numerical Analysis, SIAM J. 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.

摘      要：

    This talk introduces the dynamic stochastic bilevel optimization (DSBO), where the upper level is an ordinary differential equation and the lower level is multiobjective optimization. The DSBO provides a unified modeling 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 DSBO in the space of continuously differentiable functions with the space of measurable functions. The first class is defined by strongly convex optimization problems in the lower level, and the second class pertains to a box-constrained quadratic optimization with a Hessian P-matrix in the lower level. We develop sample average approximation (SAA) and time-stepping schemes to compute a solution of DSBO. The uniform convergence and exponential convergence are established for the SAA under suitable conditions. A time-stepping Anderson acceleration method is proposed to solve the differential variational inequality arising from the SAA of the DSBO.

          欢迎老师、同学们参加、交流！