ECSE 507

Instructor: Joshua Flynn
Office Hours: immediately after class or by scheduling
Office: BURN 1244
Course Syllabus: This webpage
Primary Textbook: Convex Optimization, by Boyd & Vendenberghe
(Free pdf found here)
Lecture Notes: here
(see here for version for presenting in class; this is updated first.)

Supplementals

(N.B.: hyperlinks may break.)

Textbooks
Anderson, Moore: Optimal Control Linear Quadratic Methods
Balakrishnan, Boyd, Feron, Ghaoui: Linear Matrix Inequalities in System and Control Theory (pdf)
Kirk: Optimal Control Theory: An Introduction (link)
Sontag: Mathematical Control Theory (link)
Exercises
Boyd, Vandenberghe: Additional Exercises for Convex Optimization (link). We’ll use the August 27, 2023 version. Please keep an eye out if it is updated.
Papers/Surveys
Baez, Erbele: CATEGORIES IN CONTROL (link, some abstract nonsense)
Boyd, Vandenberghe: Semidefinite Programming (pdf)
Boyd, Kim, Vandenberghe, Hassibi: A tutorial on geometric programming (pdf)
Ogura, Kishida, Lam: Geometric Programming for Optimal Positive Linear Systems
Klinger, Mangasarian: Logarithmic Convexity and Geometric Programming
Pisinger: The quadratic knapsack problem—a survey

Course Schedule

Key:
CO = Convex Optimization, by Boyd & Vendenberghe
AE = Additional Exercises for Convex Optimization (link), by Boyd & Vendenberghe

Week 1 (Jan 5)
Reading: Start CO Chp 2.
Optional reading: CO Chp 1.
Assignment 1: CO 2.16, 2.26, 2.35, 3.1, 3.5.
Optional: AE 3.79; Classify the convex, affine and conic hulls of three points in the plane.
Due: Jan 14.

Week 2 (Jan 10 & 12)
Reading: Finish CO Chp 2, start CO Chp 3.
Assignment 2: CO 3.7, 3.11, 3.16(a)&(b), 3.30, 3.36(d).
Optional: AE 3.13
Due: Jan 21.

Week 3 (Jan 17 & 19)
Reading: Finish CO Chp 3, start CO Chp 4.
Assignment 3: CO 4.6, 4.9, 4.12 (three problems this week.)
Optional: CO 4.4, 4.16;
Let $f:\mathbb{R}^n \to \mathbb{R}$ be such that $\nabla^2 f$ exists everywhere, but $f$ is not necessarily twice Frechet differentiable. Prove or disprove: $f$ is convex iff $z^T \nabla^2 f(x) z \geq 0$ for all $z \in \mathbb{R}^n$ and $x \in \text{dom}\, f$ . N.B.: there are convex functions where $\nabla^2 f$ is not symmetric everywhere, i.e., $\nabla^2 f \notin \boldsymbol{S}^n$ , let alone $\boldsymbol{S}_+^n$ .
Due: Jan 28.

Week 4 (Jan 24 & 26)
Reading: Continue reading CO Chp 4.
Assignment 4: CO 4.35, 4.39 (for (c), consult CO’s A.5.5), 4.43(a)(b)
Optional: CO 4.41, AE 4.23
Due: Feb 4

Week 5 (Jan 31 & Feb 2)
Reading: Finish CO Chp 4 and start CO Chap 5.
Assignment 5: CO 5.1, 5.13, 5.14
Optional:
Due: Feb 11

Week 6 (Feb 7 & 9)
Reading: Finish CO Chap 5
Assignment 6: CO 5.26, 5.27, 5.30 (you can use results from A.4.1)
Optional: AE 5.14
Due: Feb 18

Week 7 (Feb 14 & 16)
Reading: Start CO Chap 9
Assignment 6: CO 9.3, 9.5, 9.6
Optional: AE 9.1
Due: Feb 25

Week 8 (Feb 21 & 23)
Reading: Continue CO Chap 9

Week 9 (Feb 28 & Mar 1)
Reading: Finish Co Chap 9

Week 10 (Mar 6 & 8)
Spring Break

Week 11 (Mar 13 & 15)
Reading: Start CO Chap 10
Assignment 7: CO 9.8, 9.11, 10.5
Due: March 24

Week 12 (Mar 20 & 22)
Reading: Finish CO Chap 10

Course Description

Electrical Engineering : General introduction to optimization methods including steepest descent, conjugate gradient, Newton algorithms. Generalized matrix inverses and the least squared error problem. Introduction to constrained optimality; convexity and duality; interior point methods. Introduction to dynamic optimization; existence theory, relaxed controls, the Pontryagin Maximum Principle. Sufficiency of the Maximum Principle.

The optimization part of the course will primarily come from Boyd & Vendenberghe’s text. The control part may come from Kirk’s or the text of Balakrishnan, Boyd, Feron, & Ghaoui.

To get the most out of the course, it is strongly encouraged that you spend time on the readings and problems. Light reading is expected for some of the assignments (this will usually mean one needs to spend a few minutes learning a definition/example and then applying it to a problem).

Course Roles and Goals

Goal: students complete the course with a satisfactory degree of understanding of convex optimization and optimal control.
Readings: To reinforce topics covered in lecture or introduce topics not covered in lecture.
Lectures: To highlight important parts of the textbooks and prepare students for the assignments or readings.
Assignments: To provide practice and challenge any latent misunderstandings. Problems may be relevant to reading material not covered in lecture.

Homework

Submit your solutions on the MyCourses page.
Weekly problem set of 5 mandatory problems and a couple optional problems.
Due dates are indicated in course schedule.
Portion of problem set will be graded on completion (dependent on registration size).

Final

Final prompt will be released near end of semester.
You will have a week or two to complete it.

Grading

Homework: 50%
Final: 50%

This course will follow the standard McGill University grading scheme:

A	4.0	85 – 100%
A-	3.7	80 – 84%
B+	3.3	75 – 79%
B	3.0	70 – 74%
B-	2.7	65 – 69%
C+	2.3	60 – 64%
C	2.0	55 – 59%
D	1.0	50 – 54%
F (Fail)	0	0 – 49%