Optimisation Geometry: An Overview

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• Prof. Jonathan Manton, University of Melbourne
• Wednesday 22 January 2020, 12:00-13:00
• Room 611, EEE Building.

If you have a question about this talk, please contact e.kerrigan.

Myriad problems in signal processing are treated as once-off optimisation problems when they are actually real-time optimisation problems. Real-time optimisation problems can be solved more efficiently than once-off optimisation problems because the class of cost functions is known beforehand and is finite-dimensional. This means the class of cost functions can be studied beforehand, making it possible to development a bespoke real-time optimisation algorithm for each specific optimisation problem. In other words, the real-time algorithm itself can be optimised, at least conceptually.

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.

Professor Jonathan Manton holds a Distinguished Chair at the University of Melbourne with the title Future Generation Professor. He is also an adjunct professor in the Mathematical Sciences Institute at the Australian National University, a Fellow of the Australian Mathematical Society (FAustMS) and a Fellow of the Institute of Electrical and Electronics Engineers (FIEEE). He received his Bachelor of Science (mathematics) and Bachelor of Engineering (electrical) degrees in 1995 and his Ph.D. degree in 1998, all from The University of Melbourne, Australia. 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 served as an Associate Editor for the IEEE Transactions on Signal Processing and a Lead Guest Editor for the IEEE Transactions on Selected Topics in Signal Processing. He has been a Committee Member of the IEEE Signal Processing for Communications (SPCOM) Technical Committee, and a Committee Member on the Mathematics Panel for the ACT Board of Senior Secondary Studies in Australia. Currently he is a Committee Member of the IEEE Machine Learning for Signal Processing (MLSP) Technical Committee. 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).

This talk is part of the COMMSP Seminar series.

This talk is included in these lists:

• COMMSP & CP list
• COMMSP Seminar
• Room 611, EEE Building
• SAP Talks

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