University of Birmingham > Talks@bham > Optimisation and Numerical Analysis Seminars > Geometry of First-order Proximal Splitting Methods and Beyond

Geometry of First-order Proximal Splitting Methods and Beyond

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If you have a question about this talk, please contact Sergey Sergeev.

First-order proximal splitting methods are widely used in many fields through science and engineering, such as compressed sensing, signal/image processing, data science, machine learning and statistics, to name a few. Over the past decades, motivated by problems arising from these fields, modern optimisation has experienced a tremendous growth. Spectacular progress has been made in people’s understanding of optimisation problems and, in particular, of convex programming which is suitable for a wide spectrum of important problems in science and engineering. In this talk, I will present a geometric perspective of first-order methods when applied to non-smooth optimisation. Based on Riemannian geometry, several geometric characterisations of first-order methods are provided, from which we can design generic frameworks for the local linear convergence and adaptive acceleration of first-order methods. Concrete examples from inverse problems, image processing and machine learning will be used to demonstrate the state-of-the-art performance of the obtained results.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

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