Mathematics Colloquium: Professor Jonathan Manton
Topic: Optimisation Geometry: An overview
We study the problem of developing bespoke real-time optimisation algorithms from the geometric perspective. Specifically, we study the geometry of the class of cost functions (and not the geometry of each individual cost function). Interestingly, this immediately departs from the conventional wisdom that "convex is easy, non-convex is hard" because there are many examples of "easy" real-time optimisation problems where each individual cost function is non-convex. We call this endeavour Optimisation Geometry (by analogy with Information Geometry that studies the geometry of a family of probability measures). This talk gives an overview of Optimisation Geometry. It starts with a general discussion then focuses on a particular application known as the time-of-arrival problem in the signal processing literature.
About the speaker
Professor Jonathan Manton (University of Melbourne)
Professor Jonathan Manton holds a Distinguished Chair at the University of Melbourne with the title Future Generation Professor. He is also a Fellow of the Australian Mathematical Society (FAustMS) and in 2005 he became a full Professor in the Research School of Information Sciences and Engineering (RSISE) at the Australian National University. From mid-2006 till mid-2008, he was on secondment to the Australian Research Council as Executive Director, Mathematics, Information and Communication Sciences. He has been a Committee Member on the Mathematics Panel for the ACT Board of Senior Secondary Studies in Australia. Awards include a prestigious Queen Elizabeth II Fellowship and a Future Summit Australian Leadership Award. His principle fields of interest are Mathematical Systems Theory (including Signal Processing and Optimisation), Geometry and Topology (Differential and Algebraic), and Learning and Computation (including Systems Biology, Systems Neuroscience and Machine Learning).