This is the course website for Mathematical and Numerical Optimization (최적화의 수학적 이론 및 계산), 3341.454, Fall 2022.

- No class on 11/14 and 12/05.

- 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 (code1, code2)
- 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 09/14.

2.12, 2.16, 2.22, 2.28, 2.31, 2.35, 3.12, 3.14 of Boyd & Vandenberghe. - Homework 2, Due 09/20, 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 09/26, 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 10/03, 5pm. 4.15, 5.13, 5.19, 5.27 Boyd & Vandenberghe, additional problems, and 1.1, 1.4, 1.5, 1.10 of Ryu & Yin.
- Homework 5, Due 10/10, 5pm. 1.2, 1.3, 1.6, 1.9, 2.1, 2.3, 2.4, 2.5, 2.6, 2.9 of Ryu & Yin.
- Homework 6, Due 10/19, 5pm. 2.14, 2.15, 2.16, 2.20, 2.21, 2.35 of Ryu & Yin.
- Homework 7, Due 10/31, 5pm. 2.25, 2.28, 2.33, 3.1, 3.2 of Ryu & Yin.
- Homework 8, Due 11/07, 5pm. 3.5, 3.6 (You do not have to solve the erroneously unlabeled problem titled "PD3O generalizes DYS"), 3.7, 3.8, 3.13 of Ryu & Yin.
- Homework 9, Due 11/14, 5pm. 3.11, 3.14, 3.15, 3.16, 3.17 of Ryu & Yin.
- Homework 10, Due 11/21, 5pm. 9.2, 9.3, 9.5, 13.1, 13.2, 13.3, 13.5 of Ryu & Yin.
- Homework 11, Due 11/28, 5pm. 13.6, 13.8, 13.11, 13.12, 13.14, 13.20, 4.1, and 4.2 of Ryu & Yin.
- Homework 12, Due 12/07, 5pm. 2.29, 2.34, 2.36, 11.1, 11.2, 11.4, 11.8, 10.1 of Ryu & Yin.
- Homework 13, Due 12/17, 11:59pm. 11.14, 11.15, 11.17, 10.2, 10.3, 10.6, 10.7, 10.10 of Ryu & Yin.

- [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,

Jisun Park

Jaewook Suh

TaeHo Yoon

Soheun Yi

Monday and Wednesday 5:00–6:15pm at 56-106.

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

- Midterm exam: 10/22, 2:00–6:00pm, location TBD.
- Final exam: 12/20, 1:00–5:00pm, location TBD

Homework 30%, 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: Algorithms and Analyses via Monotone Operators by Ryu (myself) and Yin. You will have access to free (legal) electronic copies of both books.