Convex Analysis

Convex Analysis

This is the site for the lecture on convex analysis. The course is aimed at students of mathematics after the first year of studies. It takes place in d-dimensional real space and does not assume any prior knowledge beyond introductoyry analysis and linear algebra. 

The following lectures are already available. Each headline corresponds to one lecture of about 70 to 90 minutes and a recording is available on YouTube. Each lecture corresponds to exactly one section in the lecture note. The full lecture notes will be published after the course.

  1. Convex sets
  2. Hyperplanes and cones
  3. Projection and separation
  4. Convex functions
  5. Characterization of convex functions
  6. Continuity of convex functions and minimizers
  7. Inf-projection and inf-convolution
  8. Proximal mappings and Moreau-Yoshida regularization
  9. Subgradients

The lecture notes up to Section 9  are available here.

Updated lecture notes up to Section 18 are here.

Updaten lecture notes up to lecture 25 are here.