SCIENTIFIC PROGRAMS AND ACTIVITIES

Hamiltonian and Gradient Flows, Algorithms and Control

Sunday, March 29 - Tuesday, March 31, 1992

Workshop Co-ordinator: Anthony Bloch

In this Workshop we intend to explore the relationship between Hamiltonian and gradient flows and problems of practical interest in algorithmic design, control theory, estimation theory, linear programming, and neural nets. Recent research has revealed a number of remarkable connections between smooth flows and discrete algorithms that arise in least squares estimation problems, combinatorial problems such as matching and sorting, and interior point methods for linear programming. A classic example in the fact that the QR algorithm for diagonalizing matrices may be viewed as the time-1 map of the Toda lattice flow.The Toda lattice is an integrable system and integrable Hamiltonian systems seem to be of particular importance. There are many other relationships of this type, and one basic goal is to obtain advances in discrete problems using a smooth framework. In addition, a number of theoretical issues in control theory and realization theory can be approached through a Hamiltonian framework. This workshop is intended to bring together a number of people working in the areas relevant to this interdisciplinary research, and to encourage interaction and further developments.

Topics that we intend to cover are:

1) Estimation problems and flows
2) Integrable systems and theoretical issues in control and realization theory
3) Relationships between gradient and Hamiltonian flows
4) Topics in linear programming
5) The theory of polytopes
6) Combinatorial problems
7) Neural Nets
8) Discrete integrable systems