Feb 24 2020

Analysis and Applied Mathematics Seminar: Studying dynamics using computational polynomial optimization, by David Goluskin

February 24, 2020

4:00 PM - 4:50 PM

Location

636 SEO

Address

Chicago, IL

David Goluskin (University of Victoria): Studying dynamics using computational polynomial optimization

Many complex systems are governed by nonlinear ODEs or PDEs that cannot be solved exactly. Various properties of such solutions can be inferred by constructing auxiliary functions satisfying suitable inequalities. The most familiar example is the construction of Lyapunov functions to infer stability of particular states, but similar approaches can produce many other types of mathematical statements, including for systems with chaotic or otherwise complicated behavior. Such statements include estimates of time-averaged quantities and extreme transient behavior, approximation of nonlinear stability properties, and design of controls. In many cases, the search for the auxiliary function that implies the strongest mathematical statement can be posed as a convex optimization problem. Such problems can be studied analytically or computationally, but in most cases computation is needed to find solutions that are close to optimal. Of particular use are computational methods of polynomial optimization, where the optimization constraints include polynomial inequalities. This talk will provide an overview of different ways in which auxiliary functions can be used to study nonlinear ODEs and PDEs, as well as how polynomial optimization can be used to implement these methods computationally. Methods will be illustrated using applications to various complex systems.

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Contact

Ian Tobasco

Date posted

Feb 18, 2020

Date updated

Feb 18, 2020

Speakers

David Goluskin | (University of Victoria)