Analysis Seminar

Global-in-time Solvability of Mean-Field Control Problems and Related Equations

Speaker: Tak Kwong Wong, The University of Hong Kong

Location: Warren Weaver Hall 1314

Date: Wednesday, April 3, 2024, 3:30 p.m.


Mean-field theory provides an effective approximation of interactions among a
huge amount of agents, and hence, makes the study of optimal control
problems with numerous agents becoming feasible in both mathematical
analysis and numerical simulations. The mean-field type control problems arise
from various real-world applications, in which all the numerous agents
collaborate to optimize a single ultimate objective function, and play a crucial
role in understanding social planner problems, electricity networks, residual
neural networks (ResNet) with batch normalization, etc. In this talk, we will
first introduce the first-order mean-field type control problems in a generic
setting, and then discuss the global-in-time solvability of these problems and
their differential equations. If time permits, new results in mean field games
will also be discussed.
This is a joint work with Alain Bensoussan, Phillip Yam, and Hongwei Yuan.


Special Analysis Seminar