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

  • Location: E.N.S., 45 rue d'Ulm, 75005 Paris. Amphi Dussane

  • Schedule (2018-2019): Mondays from 13h30 until 16h30.

    • Oct. 2018: 1, 8, 15, 22 (no class on Oct. 29).

    • Nov. 2018: 5, 12.


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




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

  • DM1: Due Monday October 15 in class. From the Convex Optimization textbook: Ex. 2.12, 3.21, 3.32, 3.36

  • DM2: Due Monday October 22 in class. Homework 2

  • DM3: Due Monday November 12 before class. Homework 3. Please mail your code to in a single zip file called For numerical exercises, you can use Juliabox if you don't have access to a machine with MATLAB, Python or Julia.


Final exam, in class, November 26 2018, 9h00-12h00 amphi Curie at ENS Cachan.
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.