- RMITOpt Seminar – Andrew Eberhard (RMIT)
- AMSI Optimise 2019 – Hyatt Regency Perth
Speaker: Dr. James Saunderson – Monash University
Title: Hyperbolic cubic polynomials
Date and Time: Friday, April 26th, 3.00pm – 4.00pm
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus
|Abstract: Hyperbolic polynomials are multivariate homogeneous polynomials with certain real-rootedness properties. These give rise to a class of efficiently solvable optimisation problems called hyperbolic programs, which generalize semidefinite programs.
In this talk I’ll introduce these ideas and then focus on the case of hyperbolic polynomials of degree three (i.e. hyperbolic cubics). In particular I plan to discuss questions like “How hard is it to decide hyperbolicity of a cubic?” and “Can (powers of) hyperbolic cubics always be expressed in terms of determinants?”. We will see that (sums of squares relaxations of) polynomial optimisation problems on the sphere play an important role in studying these questions.
Bio: James Saunderson is a Lecturer in the Department of Electrical and Computer Systems Engineering at Monash. He obtained a PhD in Electrical Engineering and Computer Science from MIT in June 2015. Before joining Monash he was a postdoc in Electrical Engineering jointly at Caltech and the University of Washington.