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: 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.


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



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



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.


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.