CCIMI Short course: First-order methods for large scale optimisation problems

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This short course is organised by the CCIMI and open to all. Lectures run 14:00-16:00, Monday 4th, Friday 8th, Monday 11th and Friday 15th June.

Instructor: Stephen Becker, University of Colorado

First-order methods for large scale optimisation problems

In four two-hour lectures, we will cover (1) convex analysis, (2) convex optimization problems and optimality, (3) modern first-order methods for structured convex problems, and (4) additional large-scale algorithms. The first two lectures are designed to give the audience the necessary background, then the heart of the course starts in the third lecture which explains in detail the fast proximal gradient methods (and variants) that are the backbone of a major school of optimization. The final lecture is less analytical and gives a broad survey of useful optimization methods. The focus is primarily on convex optimization. There will be a few interludes throughout the course, such as a hands-on programming tutorial, examples of problems in machine learning and related fields, and non-convex optimization. We assume the audience is familiar with linear algebra and real analysis, but require no optimization background. Some (optional) ‘homework’ exercises will be provided through the course.