Mathematical and Numerical Optimization, Fall 2022

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

Announcements

  • No class on 11/14 and 12/05.

Lecture material

Homework

Weekly homework assignments should be submitted through eTL.

  1. Homework 1, Due 09/14.
    2.12, 2.16, 2.22, 2.28, 2.31, 2.35, 3.12, 3.14 of Boyd & Vandenberghe.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Homework 6, Due 10/19, 5pm. 2.14, 2.15, 2.16, 2.20, 2.21, 2.35 of Ryu & Yin.
  7. Homework 7, Due 10/31, 5pm. 2.25, 2.28, 2.33, 3.1, 3.2 of Ryu & Yin.
  8. 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.
  9. Homework 9, Due 11/14, 5pm. 3.11, 3.14, 3.15, 3.16, 3.17 of Ryu & Yin.
  10. Homework 10, Due 11/21, 5pm. 9.2, 9.3, 9.5, 13.1, 13.2, 13.3, 13.5 of Ryu & Yin.
  11. 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.
  12. 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.
  13. 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.

Lecture Plans and Reading

  • [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

Course Information

Instructor

Ernest K. Ryu, 27-205,

Photo of Ernest Ryu

Graduate Teaching Assistants

Jisun Park

Photo of Jisun Park

Jaewook Suh

Photo of Jaewook Suh

TaeHo Yoon

Photo of TaeHo Yoon

Undergraduate Teaching Assistants

Soheun Yi

Photo of Soheun Yi

Lectures

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

Exams

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

Grading

Homework 30%, midterm exam 30%, final exam 40%.

Prerequisites

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.

Textbooks

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.