First-order methods in optimization

Lecturer

Amir Beck, Tel Aviv University

Web Page

Schedule and place

This 15-hour course will take place in 6 sessions over three days on December 7, 8, 9, 2021 at UCLouvain, Euler building, 4 Avenue Georges Lemaître, 1348 Louvain-la-Neuve (room A002, ground floor).

Schedule : 5.30 hours/day

December 7: from 9:45 to 12:30 and from 15:00 to 17:45 (including a 15-minute coffee break in each session).

December 8: from 9:45 to 12:30 and from 14:00 to 16:45 (including a 15-minute coffee break in each session). 

December 9: from 9:45 to 12:30 and from 14:00 to 16:45 (including a 15-minute coffee break in each session). 

Travel instructions are available here.

Description

The purpose of the course is to explore the theory and application of a wide range of proximal-based methods. First, we will review the basic theoretical background from convex analysis needed to understand proximal-based methods, including subgradients, conjugate functions and proximal operators. Then, in the central part of the course, we will explore several algorithms, including proximal gradient, dual proximal gradient, acceleration techniques, smoothing approaches, block decomposition variants and various splitting methods, including Lagrangian-based methods. The theoretical emphasis will be on the complexity results. On the applied side, implementation issues and applications will be discussed.

Knowledge of a first course in optimization (convexity, optimality conditions, duality…) will be assumed.

Course material

TBD

Evaluation

TBD