ECE1505: Convex Optimization (Winter 2026)
Instructor: Professor Wei Yu
Lectures: Thursday 9:10am-12noon SS-1085
(NOTE: There is some classroom assignment mixed-up that needs to be resolved by the ECE graduate office. The above classroom is likely not the correct lecture room. Please check this page again in the first week of 2026.)
TA: Yuanxin Guo (yuanxin.guo@mail.utoronto.ca) and Yiming Liu (eceym.liu@mail.utoronto.ca)
Textbook: Convex
Optimization
Authors: Stephen Boyd and Lieven
Vandenberghe, Cambridge University Press, 2004
This course provides a comprehensive coverage of the theoretical foundation and numerical algorithms for convex optimization. The topics covered in this course may be of interests to students in all areas of engineering and computer science.
The great watershed in optimization isn't between linearity and nonlinearity, but convexity and nonconvexity - R. Tyrell Rockafellar (SIAM Review '93)
Pre-requisite: Vector calculus. Linear algebra. A fair level of mathematical maturity is expected.
Course Outline and Homework:
|
Week |
Topics |
Text Reference |
Assignments |
|
1/08 |
Introduction; Motivating Example: Data Fitting. Basic Concepts: Vector Space, Norm, Vector Calculus, Linear Algebra. |
Chapter 1 Appendix A |
|
|
1/15 |
Gradient and Hessian of functions. Functions of matrices. Convex Sets. |
Chapter 2 |
HW #1 Due Jan 27 |
|
1/22 |
Convex functions. First-order and Second-order conditions for differentiable convex functions. Properties of Convex Functions. |
Chapter 3 |
|
|
1/29 |
Convex optimization problems. Local and global optimal solutions of convex optimization problems. |
Chapter 4 |
|
|
2/05 |
Linear Programming. Quadratic programming. Quadratically constrained quadratic programming. Second-order cone programming. Robust linear programming. |
Chapter 4 |
HW #2 Due Feb 24 |
|
2/12 |
Least-squares problems. Optimal control problem. Geometric programming. Semi-definite programming. SDP relaxation. |
Chapter 4 |
|
|
|
Study Break |
|
|
|
2/26 |
Theory: Lagrangian. Dual optimization problem. Duality gap. Slater’s condition. Sensitivity analysis. |
Chapter 5, Rockafellar: Sec. 33 |
Project Proposal Due March 10 |
|
3/05 |
Dual of LP. Economics and Pricing Interpretation. Saddle points. Game theory. Duality theory for minimax optimization. |
Chapter 5, Rockafellar: Sec. 33 |
|
|
3/12 |
Dual of QP. Controllability-observability duality. Dual of $l_p$ optimization. Duality theory for optimization problem with generalized inequality. SDP relaxation. |
Chapter 5 |
HW #3 Due March 24 |
|
3/19 |
Complementary slackness condition. Karush-Kuhn-Tucker (KKT) Conditions. Interpretation of the KKT condition. Regularity condition for local optimality. |
Bertsekas Ch. 3 |
|
|
3/26 |
Algorithms: Descent methods. Newton's method. Equality Constrained Minimization. Infeasible-start Newton's Method. Interior-point method for constrained optimization. |
Chapter 9 Chapter 10 Chapter 11 |
|
|
4/02 |
Interpretation of Interior-point method via KKT condition. Primal-Dual Interior-Point Method. Generalized Inequality. Analytic Centering. Ellipsoid method. Subgradient method for non-differentiable functions. Dual Decomposition. Coordinate descent. |
Chapter 11 |
HW #4 Due April 7 |
|
|
|||
|
|
Final Exam: Tentatively the week of April 14 |
|
Project Report Due April 14 |
Project Information: Click here
Grades: Homework (25%), Final Exam (50%), and Course Project (25%). No late homework or project are accepted.
References:
Last Updated: December 28, 2025