## 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: Mondays 13:30-16:30, E.N.S., 29 rue d'Ulm, 75005 Paris, Amphi Jean Jaurès. Oct. 2021: 4, 11, 18. Nov. 2021: 8, 15, 22.
## OrganisationThe course will be live but course videos from 2020 are available below. Introduction (40 minutes) Convex Sets (32 minutes) Convex Functions (49 minutes) Convex Optimization Problems (51 minutes) Duality (120 minutes) Unconstrained Optimization (59 minutes) Equality Constrained Optimization (29 minutes) Barrier Method (53 minutes) First Order Methods Part I (33 minutes) First Order Methods Part II (47 minutes) Applications (55 minutes) SDP Applications (26 minutes) 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. We will be using Gradescope to grade assignments. In order to submit your work, you must create a Gradescope account. Please ensure you do so with your full name. You will then be able to join the course using course number P5JJRD. Late homework will not be graded. DM1: Due Monday October 11 before class. Homework 1 DM2: Due Monday November 8 before class. Homework 2 DM3: Due Monday November 29. Homework 3. Please submit your code on Gradescope. For numerical exercises, you can use either Julia, Python or MATLAB.
## ExamFinal exam, on Monday Dec. 6 2021, 13:30-16:30, salle 1G58 (grand amphi) |