First-order methods in optimization


Amir Beck, Tel Aviv University

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Schedule and place

This 15-hour course will take place in five sessions over three days on June 7,8,9 2022

at UCLouvain - Salle Carnoy (B059) - Bâtiment Carnoy, Croix du Sud, 4-5 Louvain-la-Neuve

Travel instructions are available here


  • June 7: from 09:15 to 12:30
  • June 7: from 13:45 to 17:00
  • June 8: from 09:15 to 12:30
  • June 8: from 13:45 to 17:00
  • June 9: from 09:15 to 12:30 

Including a 15-minute coffee break in each session

Teaching method: Face-to-face 


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


Evaluation based on the submitted solutions of a set of exercises.