S&DS 432b/632b: Advanced Optimization Techniques (Spring 2025)

Course Description: This course covers fundamental optimization algorithms and their theoretical analysis, emphasizing convex optimization. Topics covered include gradient descent and acceleration; lower bounds; structured problems; Newton's method; and interior point methods. Prerequisites: Knowledge of linear algebra, such as MATH 222/225; multivariate calculus, such as MATH 120; probability, such as S&DS 241/541; optimization, such as S&DS 431/631; and comfort with proof-based exposition and problem sets.

Instructor: Sinho Chewi (sinho.chewi@yale.edu)

References

• [B] S. Bubeck, Convex optimization: algorithms and complexity (2015).
• [NN] Y. Nesterov and A. Nemirovskii, Interior-point polynomial algorithms in convex programming (1994).

Schedule

The course meets on Tuesdays and Thursdays, 1–2.15 p.m., in TBA. I will also be available for an hour after each class if you have any questions or if you would like to discuss. If these times do not work for you, or if you have any other concerns, please reach me via email.

Assignments

Grades are based solely on four or five problem sets (to be determined) and one take-home final exam. Tentatively, the problem sets will be released on TBA, and each one is due roughly one and a half weeks after it is assigned.

Please feel free to work on the problem sets with others, but list your collaborators at the beginning of your submission. Problem sets should be typed in LaTeX and submitted via Gradescope (the link can be found in Canvas).