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

  • Schedule (2016-2017): Mondays from 13h30 until 16h30, amphi Tocqueville. First class on Oct. 3 2016.

  • Location: Amphi Tocqueville at E.N.S. Cachan. campus map.

  • Getting there: RER B, station Bagneux. See the access plan to E.N.S. Cachan.

Organisation

The course is split in three parts. Six lectures of three hours each.

  • Modelling

    • 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

Notes

Exercices

Most of the exercises are taken from the textbook by Boyd et Vandenberghe.
Please mail your HW to dm.daspremont@gmail.com, you will get an automatic delivery confirmation. Scanned handwritten documents are OK. For numerical exercises, return your code together with a few numerical experiments. You can use Juliabox if you don't have access to a machine with MATLAB, Python or Julia.

  • DM1: Due Monday October 24 at 13h30. From the Convex Optimization textbook: Ex. 2.12, 3.21, 3.32, 3.36

  • DM2: Due Monday November 7 at 13h30. Ex. 5.5, 5.7, 5.9, 5.11, 5.13.

  • DM3: Due Monday November 21 at 13h30. DM 3.

Exam

Final exam, on Friday, November 25 2016, 14h00-17h00 in class. Closed book. You are allowed one page of notes (recto-verso).