Optimisation Geometry

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Signal processing is an enabling technology for multi-billion dollar industries including broadband connections, medical imaging devices and automotive collision avoidance systems. A key component is real-time optimisation. While various aspects of real-time optimisation have been studied extensively, especially under the banner of adaptive signal processing, the general (non-adaptive) problem will be studied here from a geometric viewpoint. Morse theory and other tools from differential topology will be used to understand the inherent complexity of real-time optimisation problems and to develop novel numerical algorithms for classes of real-time optimisation problems having widespread applicability.