Preliminary list of abstracts

Note: We are using the fantastic MathJax JavaScript library to typeset the mathematics on this web page. You can right-click on a formula to zoom in or to select the rendering engine you like (all under 'Settings'). Under Firefox the default renderer turns out to be MathML (which is quick), but you might prefer the HTML-CSS renderer for more faithful LaTeX rendering. If you encounter any problems with this setup: then please email us!

Click here to go back to the list of abstracts.

An Adaptive Sparse Grid scheme for HJB equations
Keywords: HJB equations; Sparse Grids; Optimal Control
Mon, 09:50--10:15
  • Klompmaker, Irene (Institut fuer Mathematik, TU Berlin, Germany)
  • Bokanowski, Olivier (Universit√© Paris-Diderot, France)
  • Garcke, Jochen (TU Berlin, Germany)
  • Griebel, Michael (Universit√§t Bonn, Germany)

We consider an adaptive sparse grid approach for the numerical solution of Hamilton-Jacobi-Bellman equations in high dimensions. HJB equations arise for example for the solution of optimal control problems. We concentrate on equations of the form that describe problems in continuous time and state space with finite time horizon. We use spatial adaptive sparse grids for the discretization of the continuous state spaces and apply a semi lagrangian scheme based on the dynamic programming approach in order to approximate the HJB-solution. We show numerical results where sparse grids enable us to treat problems in up to 6 dimensions.