Date

Topics

Optional reading

Linear algebra and convex analysis background

3/5

Lec 1 Linear algebra review

LMCO Appendix A

3/7

Lec 2 Elementary convex analysis I

CC 1.1–1.2, 2.1–2.8, 2.12

3/12

Spring break no classes

3/14

Spring break no classes

3/19

Lec 3 Elementary convex analysis II

CC 1.1–1.2, 2.1–2.8, 2.12

Conic programming

3/21

Lec 4 Conic programming I

LMCO 1.1, 1.2, 1.4

3/24

Pset 1 Due [Pset 1] [solutions]

3/26

Lec 5 Conic programming II

LMCO 1.4

Conic programming applications

3/28

Lec 6 SOCP representability

LMCO 2.1–2.3

4/2

Lec 7 SDP representability

LMCO 3.1, 3.2

4/4

Lec 8 SDP relaxations of intractable problems

CC 4.10–4.11, LMCO 3.3–3.4
[Blekherman, Parrilo, and Thomas’ Textbook] See Chapter 2.2 for additional SDP applications
[Hamza Fawzi’s Lecture Notes] See Lectures 10–13 for additional SOS

4/7

Pset 2 Due [Pset 2] [solutions]

First-order methods for smooth minimization

4/9

Lec 9 Subgradient descent, gradient descent, accelerated gradient descent

LCO 3.1.5, 3.2.3

4/11

Lec 10 Subgradient descent, gradient descent, accelerated gradient descent

LCO 2.1.1, 2.1.3, 2.1.5, 2.2
[Ahn Sra 2022] On PPM and AGD
[Dmitriy Drusvyatskiy’s Lecture Notes] See 5.3, 6.1, 6.2

4/16

Lec 11 Oracle lower bounds

LCO 3.2.1, 2.1.2, 2.1.4

4/18

Lec 12 Convex conjugates and performance estimation programming

FOMO 4
[Drori Teboulle 2012] On PEP

4/21

Pset 3 Due [Pset 3] [solutions]

Other topics in first-order methods

4/23

Lec 13 Mirror descent

FOMO 9

4/25

Lec 14 Frank–Wolfe Method

[Sebastian Pokutta’s blog] On Frank–Wolfe and extensions (see posts 2–4)
[Garber Hazan 2015] On an extension of Frank–Wolfe

5/2

Pset 4 Due [Pset 4] [solutions]