## 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