Joint DE+Optimization Seminar: Jinglai Shen (UMBC)
Department Faculty Presentations
Location
Mathematics/Psychology : 401
Date & Time
November 14, 2022, 11:00 am – 12:00 pm
Description
Title: Dynamic Stochastic Variational Inequality and Its
Computation
Abstract: In
this talk, we introduce the dynamic stochastic variational inequality (DSVI).
The DSVI is an ODE whose right hand side is defined by a natural mapping of a
VI (referred to as the first-stage VI) and is coupled with another stochastic
VI (referred to as the second-stage SVI). The DSVI provides a unified modeling
framework for various applications involving equilibrium/optimality conditions
(VI), dynamics (ODE), and uncertainties (stochasticity). We establish
solution existence and uniqueness for two classes of DSVIs: the first class is
defined by a strongly monotone SVI in the second stage, and the second class
pertains to a box-constrained stochastic linear VI with the P-property in the
second stage. Preliminary results on switching dynamics of the DSVI are
presented. We develop sample average approximation (SAA) and time-stepping
schemes to compute the DSVI. The uniform convergence and exponential
convergence are established for the SAA under suitable conditions. A
time-stepping EDIIS (energy direct inversion on the iterative subspace) method
is used to solve the differential VI arising from the SAA of the DSVI. Our
results are illustrated by an instantaneous dynamic user equilibrium
problem arising from transportation engineering. This is a joint work with Dr.
Xiaojun Chen of the Hong Kong Polytechnic University.