Advanced Optimization (Spring 2026)
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 12:30 - 1:45 PM at HN 130
Teaching Assistant
- TA: Jaehyuk Kwon
- Email: jaehyuk@unc.edu
Course Information
Useful Links
Tentative Course Schedule
| Date | Week# | Topic | HW# | Event |
| 8-Jan | 1 | Smooth Functions, Open Sets | Syllabus | |
| 13-Jan | 2 | Nonlinear and Polynomial Optimization | ||
| 15-Jan | 2 | Semi-definite Optimization, Sums of Squares | 1 | |
| 20-Jan | 3 | Sums of Squares, Second-order Conic Optimization | ||
| 22-Jan | 3 | Second-order Conic Optimization, Lagrangian Duality | 2 | |
| 27-Jan | 4 | Duality, Saddle Points | ||
| 29-Jan | 4 | Saddle Points, Strong Duality | ||
| 3-Feb | 5 | Strong Duality For Convex Optimization | ||
| 5-Feb | 5 | Strong Duality for Semi-definite Optimization | 3 | |
| 10-Feb | 6 | Strong Duality For Semi-definite Optimization | ||
| 12-Feb | 6 | Optimality Conditions For Semi-definite Optimization, Weak Infeasibility | ||
| 17-Feb | 7 | Weak Infeasibility,Conic Optimization | ||
| 19-Feb | 7 | Asymptotic Farkas Lemma | 4 | |
| 24-Feb | 8 | Asymptotic Strong Duality | ||
| 26-Feb | 8 | Strong Duality For Conic Optimization | ||
| 3-Mar | 9 | Newton's Method, Algebraic Sets, Singularity | ||
| 5-Mar | 9 | Exam | 5 | Midterm |
| 10-Mar | 10 | Interior Point Methods For Linear Optimization | ||
| 12-Mar | 10 | Predictor-Corrector Interior Point Method, Central Path | ||
| 17-Mar | 11 | No Class | Spring Break | |
| 19-Mar | 11 | No Class | Spring Break | |
| 24-Mar | 12 | Existence of Central Path, Implicit Function Theorem | ||
| 26-Mar | 12 | Semi-algebraic Sets and Functions, Semi-algebraic Implicit Function Theorem, Convergence of Central Path | 6 | |
| 31-Mar | 13 | Real and Bit Complexity in Polynomial and Semi-definite Optimization | ||
| 2-Apr | 13 | No Class | Well-Being Day | |
| 7-Apr | 14 | Optimality Conditions for Unconstrained Optimization | ||
| 9-Apr | 14 | First-order and Second-order Conditions | 7 | |
| 14-Apr | 15 | First-order and Second-order Conditions - Fritz John Conditions | ||
| 16-Apr | 15 | KKT Conditions, M-F Constraint Qualifications | ||
| 21-Apr | 16 | Slater's Condition, Second-order Sufficient Conditions | ||
| 23-Apr | 16 | Sensitivity Analysis | 8 | |
| 27-Apr | End of Classes | |||
| 2-May | Final Exam (4:00 - 7:00 PM at HN 130) | |||