Numerical Methods for Optimal Control in High Dimensions

August 29 to September 2, 2005

at the

American Institute of Mathematics, Palo Alto, California

organized by

Doron Levy, Ian Mitchell, and Adam Oberman

This workshop, sponsored by AIM and the NSF, will be devoted to problems of optimal control, broadly interpreted to include stochastic control problems and differential games. These problems appear in many engineering fields, including aeronautical engineering, robotics, and process control, and in economics, in particular resource allocation and mathematical finance. It is a standard practice to formulate these problems in terms of a multi-dimensional Hamilton-Jacobi-Bellman (HJB) equation.

The workshop will focus on computational methods for tackling high dimensional HJB and related equations. These methods may include approximation of the problem by another more amenable to computation and/or numerical methods for solution of general or restricted classes of high dimensional equations. This workshop will bring together application specialists, numerical analysts and theorists that will identify open problems and discuss recent progress that has been made in application specific fields.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and working sessions.

Invited participants include M. Arisawa, W. Au, A. Bourlioux, A. Doucet, P. Dupuis, L. El Ghaoui, T. Giorgi, J. Goodman, A. Kurzhanski, H. Kushner, D. Levy, P.-L. Lions, I. Mitchell, A. Ng, A. Oberman, S. Osher, Z. Popovic, E. Rouy, T. Souganidis, C. Tomlin, A. Tourin, R. Tsai, and A. Vladimirsky.

The deadline to apply for support to participate in this workshop has passed.

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