Master M2 MVA: Convex Optimization, Algorithms and Applications.


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.


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




Most of the exercises are taken from the textbook by Boyd et Vandenberghe.
Please mail your HW to, 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.


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