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 turn in your home work in class. Late homework will not be graded.


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.