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

  • Location: the course will be inverted this year, with recorded lectures posted on this website and an online Q&A held on regular class days.

  • Q&A schedule (2020-2021): Mondays at 14:00 by videoconference.

    • Oct. 2020: 5, 12, 19.

    • Nov. 2020: 2, 9, 16.

Organisation

Course videos will be available here.

Notes

Program

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

References

Exercices

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

  • DM1: Due Monday October 19 before class. From the Convex Optimization textbook: Ex. 2.12, 3.21, 3.32, 3.36

  • DM2: Due Monday November 2 before class. Homework 2

  • DM3: Due Monday November 23. Homework 3. Please mail your code to dm.daspremont@gmail.com in a single zip file called lastname-firstname-DM3.zip. For numerical exercises, you can use either Julia, Python or MATLAB.

Exam

Final exam due on December 2 at 14:00. Please mail your scanned exam exam (in B&W), together with zipped code, to dm.daspremont@gmail.com.