I taught this lecture at ETH in 2009-2014, at University of Zurich in 2015, and, in the present version at ETH in 2018.

Warning: this lecture is not for the faint of heart superficially seduced by the terms "machine learning" and "computational finance" in the official title. The last time I gave it, it was inexplicably open to bachelor students and without a teaching assistant to guide the courageous learner through the exercises. Brave were the survivors among bachelor students.

The targeted audience is mature Master students and PhD Students in Mathematics, Engineering, and Finance.

I've immensely enjoyed teaching this course over the years.

Part 1: Convex analysis

1. Introduction, Convex Sets

2. The SDP Cone, Separation theorems

3. Duality

4. Optimality conditions, Lagrangian Duality

5. Subgradients, Conjugate functions

6. KKT Conditions and Applications

Part 2: Applications

1. Conic Optimization and Applications

2. More Applications (Approximations, Coalitions and convex games, Statistical Estimation)

Part 3: Algorithms

1. Black-box Methods 1 (Gradient and Stochastic Gradient for convex optimization)

2. Black-box Methods 2 (Accelerated gradient, gradient for non-convex problems, Newton's method, Mirror Descent)

3. Interior-Point Methods