Lecture: Convex Optimization and Online Learning (MM25)

Language: English or German, as the audience requests.

Content: This lecture covers basic concepts of convex analysis and programming (classes of convex sets and functions, duality, nonexpansive mappings, splitting of convex programs, etc) with a focus on the analysis of iterative algorithms for solving large-scale convex optimization problems. Particular attention is paid to techniques for online convex optimization and the prediction of individual sequences in unknown environments, which play a key role in machine learning applications.

The content of the lecture is targeted at students of mathematics and scientific computing with a long-term interest in machine learning, to prepare them for more advanced topics closer to research.

Prerequisites: All proofs are elementary and only require knowledge from the mandatory undergraduate courses on analysis and linear algebra.

Registration: If you wish to attend the lecture and the exercises, please sign up using MÜSLI.

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Lecture Notes: All statements (second part) will be proven in the lecture.

Convex Analysis and Programming

Online Convex Optimisation and Learning

Miscellany

Exercise Sheets

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