University COVID-19 update

The University of Waterloo is constantly updating our most Frequently Asked Questions.

Questions about buildings and services? Visit the list of Modified Services.

Please note: The University of Waterloo is closed for all events until further notice.

PhD Comprehensive Exam | Yangang Chen, Numerical Solutions of Hamilton-Jacobi-Bellman Equations with ApplicationsExport this event to calendar

Tuesday, April 26, 2016 — 1:00 PM EDT

MC 6496​

Candidate

Yangang Chen
Applied Mathematics, University of Waterloo

Title

Numerical Solutions of Hamilton-Jacobi-Bellman Equations with Applications

Abstract

This research proposal focuses on Hamilton-Jacobi-Bellman (HJB) equa- tions, which are nonlinear controlled partial differential equations (PDEs). We are interested in constructing finite difference schemes that converge to the viscosity solutions of the HJB equations, and developing solvers, and furthermore, fast solvers, for the discretized equations.

We discuss two specific applications of the HJB equations. One is to solve a Monge-Amp`ere equation by converting it to an equivalent HJB equation. Wide stencil scheme is applied to discretize the HJB equation. We prove that the numerical scheme is consistent, stable and monotone, and thus con- verges to the viscosity solution. We apply this numerical scheme to image registration problem.

Another application of the HJB equations is the oligopolistic mean field game model in economics. The optimal lifetime profits of the companies in a mean field game can be determined by a system of PDEs that contains an HJB equation. Multigrid method is employed as the fast solver for the discretized equations.

In the end of the research proposal, we summarize our progress and pro- pose some future research topics.

S M T W T F S
27
28
29
30
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
  1. 2021 (28)
    1. September (1)
    2. August (2)
    3. July (1)
    4. June (3)
    5. May (3)
    6. April (7)
    7. March (1)
    8. February (5)
    9. January (5)
  2. 2020 (31)
    1. September (1)
    2. June (2)
    3. May (10)
    4. April (2)
    5. March (6)
    6. February (4)
    7. January (6)
  3. 2019 (86)
  4. 2018 (70)
  5. 2017 (72)
  6. 2016 (76)
  7. 2015 (77)
  8. 2014 (67)
  9. 2013 (49)
  10. 2012 (19)
  11. 2011 (4)
  12. 2009 (5)
  13. 2008 (8)