Master M2 MVA: Convex Optimization, Algorithms and Applications.

Description

The objective of this course is to learn to recognize, transform and solve a broad class of convex optimization problems arising in various fields such as machine learning, finance or signal processing. The course starts with a basic primer on convex analysis followed by a quick overview of convex duality theory. The second half of the course is focused on algorithms, including first-order and interior point methods, together with bounds on their complexity. The course ends with illustrations of these techniques in various applications.

Course organization

  • Location: Mondays 13:30-16:30, E.N.S., 45 rue d'Ulm, 75005 Paris, Amphi Dussane.

    • Oct. 2021: 4, 11, 18.

    • Nov. 2021: 8, 15, 22.

Organisation

The course will be live but course videos from 2020 are available below.

Notes

Program

The course is split in three parts.

  • Modeling

    • Convex sets, functions and problems

    • Duality

  • Algorithms

    • Interior point methods

    • Complexity

    • First-order methods, acceleration

  • Applications

    • Machine learning and statistics

    • Signal processing

    • Combinatorial problems

    • Finance

References

Exercices

Many of the exercises are taken from the textbook by Boyd et Vandenberghe. Please email your PDF or scanned HW to dm.daspremont@gmail.com. Late homework will not be graded.

Exam

Final exam, on Monday Dec. 6 2021, 13:30-16:30, location TBD
Closed book. You are allowed one page of notes (recto-verso). The exam will be mostly focused on chapters 1-5 of the textbook (up to duality) Final exam 2016.