This is the course website for Mathematical and Numerical Optimization (최적화의 수학적 이론 및 계산), 3341.454, Fall 2021.

- Introduction (BV)
- Convex Sets
- Convex Functions
- Convex Optimization Problems
- Convex Duality
- Introduction and Preliminaries (RY)
- Monotone Operators and Base Splitting Schemes
- Primal-dual splitting methods
- Parallel computing
- Stochastic Coordinate Update Methods
- Duality in Splitting Methods
- Scaled Relative Graphs
- Distributed and Decentralized Optimization
- Maximality and Monotone Operator Theory
- Conclusion

Weekly homework assignments should be submitted through eTL.

- Homework 1, Due 09/10, 5pm.

2.12, 2.16, 2.22, 2.28, 2.31, 2.35, 3.12, 3.14 of Boyd & Vandenberghe.

- [Week 1] Introduction and convex sets (Reading: 1-2 BV)
- [Week 2] Convex functions (Reading: 3.1, 3.2, 3.3, 3.5 BV)
- [Week 3] Convex optimization problems (Reading: 4.1-4.4, 4.6 BV)
- [Week 4] Convex duality (Reading: 5.1-5.5, 5.7, 5.9 BV)
- [Week 5-6] Monotone operators
- [Week 7-8] Primal-dual methods
- [Week 9] Stochastic coordinate update methods
- [Week 10] Asynchronous coordinate update methods
- [Week 11] ADMM-type methods
- [Week 12] Maximality, duality
- [Week 13] Acceleration, stochastic optimization
- [Week 14] Scaled relative graphs
- [Week 15] Distributed and decentralized optimization

Ernest K. Ryu, 27-205,

Monday and Wednesday 9:30–10:45am over Zoom. Live (online) attendance is required. Meeting link and the password are available on eTL.

This class will have hand-written (no computers) in-person midterm and final exams.

- Midterm exam: Wednesday, 10/27, 8:00am–12:00pm, location TBD.
- Final exam: Wednesday, 12/15, 8:00am–12:00pm, location TBD.

Attendance 10%, homework 20%, midterm exam 30%, final exam 40%.

Good knowledge of advanced calculus, linear algebra, basic probability, and basic programming at the level of variables, loops, and functions is required. Background in (mathematical) analysis and measure-theoretic probability theory is helpful but not necessary.

We will use Convex Optimization by Boyd and Vandenberghe and Large-Scale Convex Optimization via Monotone Operators by Ryu (myself) and Yin. You will have access to free (legal) electronic copies of both books, so there is no need to purchase them.