RMITOpt Seminar – Dr. James Saunderson – Monash University

 

 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.

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