Discrete Mathematics for Data Science (Fall 2024)
Instructor
- Instructor: Ali Mohammad Nezhad
- Office: Hanes 330
- Office hours: Tuesday and Thursday 4:00 - 5:00 PM
- Email: alimn@unc.edu
Lecture
- STOR 614-001: Tuesday and Thursday 02:00 - 03:15 PM at HN 130
Teaching Assistant
- TA: Yanhui Ren
- Email: yar@unc.edu
Course Information
Useful Links
Tentative Course Schedule
| Date | Week# | Topic | HW# | Event |
| 09-Jan | 1 | Smooth functions, open sets | Syllabus | |
| 14-Jan | 2 | Nonlinear and polynomial optimization | ||
| 16-Jan | 2 | Semi-definite optimization, sums of squares | 1 | |
| 21-Jan | 3 | Sums of squares, second-order conic optimization | ||
| 23-Jan | 3 | Second-order conic optimization, Lagrangian duality | ||
| 28-Jan | 4 | Duality, saddle points | ||
| 30-Jan | 4 | Saddle points, strong duality | 2 | |
| 04-Feb | 5 | Strong duality for convex optimization | ||
| 06-Feb | 5 | Strong duality for semi-definite optimization | ||
| 11-Feb | 6 | Strong duality for semi-definite optimization | ||
| 13-Feb | 6 | Optimality conditions for semi-definite optimization, weak infeasibility | ||
| 18-Feb | 7 | Weak infeasibility,conic optimization | ||
| 20-Feb | 7 | Asymptotic Farkas lemma | 3 | |
| 25-Feb | 8 | Asymptotic strong duality | ||
| 27-Feb | 8 | Strong duality for conic optimization | ||
| 04-Mar | 9 | Newton's method, algebraic sets, singularity | ||
| 06-Mar | 9 | Interior point methods for linear optimization | ||
| 11-Mar | 10 | No Class | Spring Break | |
| 13-Mar | 10 | No Class | Spring Break | |
| 18-Mar | 11 | Predictor-corrector interior point method, central path | 4 | |
| 20-Mar | 11 | Exam | Midterm | |
| 25-Mar | 12 | Existence of central path, implicit function theorem | ||
| 27-Mar | 12 | Semi-algebraic sets and functions, semi-algebraic implicit function theorem, convergence of central path | ||
| 01-Apr | 13 | Real and bit complexity in polynomial and semi-definite optimization | ||
| 03-Apr | 13 | Optimality conditions for unconstrained optimization | ŧ | |
| 08-Apr | 14 | No Class | Talk at NC State | |
| 10-Apr | 14 | First-order and second-order conditions | 5 | |
| 15-Apr | 15 | First-order and second-order conditions - Fritz John Conditions | ||
| 17-Apr | 15 | No Class | Well-Being Day | |
| 22-Apr | 16 | KKT conditions, M-F constraint qualifications | ||
| 24-Apr | 16 | Slater's condition, second-order sufficient conditions | ||
| 28-Apr | End of Classes | |||
| 01-May | Final Exam (12:00 - 03:00 PM at HN 130) | |||