## Master M2 MVA: Convex Optimization, Algorithms and Applications.## DescriptionThe 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 organizationLocation: 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.
## OrganisationCourse videos will be available here. Monday October 5. Logistics (2 minutes) Introduction (40 minutes) Convex Sets (32 minutes) Convex Functions (49 minutes)
Monday October 12. Convex Optimization Problems (51 minutes) Duality (120 minutes)
Monday October 19. Unconstrained Optimization (59 minutes) Equality Constrained Optimization (29 minutes) Barrier Method (53 minutes)
Monday November 2. First Order Methods Part I (33 minutes) First Order Methods Part II (47 minutes)
Monday November 9. Applications (55 minutes) SDP Applications (26 minutes)
Monday November 16. l1 Penalties (16 minutes)
## Notes## ProgramThe 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
## ReferencesConvex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press. Introductory Lectures on Convex Optimization, Y. Nesterov, Springer. Lectures on Modern Convex Optimization, A. Nemirovski and A. Ben-Tal, SIAM.
## ExercicesMany 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.
## ExamFinal 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. |