This is the course website for Mathematical and Numerical Optimization (최적화의 수학적 이론 및 계산), 3341.454, Fall 2020.

- 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 09/11, 5pm.

2.12, 2.16, 2.22, 2.28, 2.31, 2.35, 3.12, 3.14 of Boyd & Vandenberghe. - Homework 2, Due 09/21, 5pm.

3.15, 3.18, 3.22, 3.24, 3.25, 3.36, 4.1, 4.11 of Boyd & Vandenberghe and an additional problem. - Homework 3, Due 09/25, 5pm.

4.4, 4.24, 4.42, 4.43, 5.3 of Boyd & Vandenberghe and additional problems, veh_speed_sched_data.py. - Homework 4, Due 10/9, 5pm.

4.15, 5.13, 5.19, 5.27 Boyd & Vandenberghe and additional problems. - Homework 5, Due 10/19, 5pm.

2.1, 2.2, 2.3, 2.5, 2.12, 2.13, 2.14, 2.15 of Ryu & Yin. - Homework 6, Due 11/6, 5pm.

Problems. - Homework 7, Due 11/16, 5pm.

Problems (full assignment uploaded on 11/6). - Homework 8, Due 11/23, 5pm.

Problems (full assignment uploaded on 11/14). - Homework 9, Due 11/27, 5pm.

Problems. - Homework 10, Due 12/8, 5pm.

Problems. - Homework 11, Due 12/16, 12pm.

Problems (full assignment uploaded on 12/8), fast_decentralized_starter.py.

- [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, .

Tuesdays and Thursdays 2:00–3:15 pm over Zoom. Live (online) attendance is required. Meeting link and the password are available on eTL.

The midterm and final exams will be take home exams.

- Midterm exam: 10/22, 2:00–6:00pm, take home exam.
- Final exam: 12/15 12:00–6:00pm, take home exam.

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