ECE1505: Convex Optimization

Electrical and Computer Engineering Department

University of Toronto

Winter 2025

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Textbook:    Convex Optimization
Authors:       Stephen Boyd and Lieven Vandenberghe, Cambridge University Press, 2004

The great watershed in optimization isn't between linearity and nonlinearity, but convexity and nonconvexity  - R. Tyrell Rockafellar (SIAM Review '93)

This course provides a comprehensive coverage of the theoretical foundation and numerical algorithms for convex optimization. Topics include:

• Convex sets and convex functions. Convex optimization problems.
• Least-square problems. Optimal control problems.
• Lagrangian duality theory.
• Karush-Kuhn-Tucker theorem. Slater's condition.
• Generalized inequalities.
• Minimiax optimization and saddle points.
• Linear programming, quadratic programming, semidefinite programming and geometric programming.
• Numerical algorithms: Descent methods, Newton's method. Interior-point method.
• Relaxation.
• Applications.

The topics covered in this course may be of interests to students in all areas of engineering and computer science.

Course Outline and Homework: Click here

Project Information: Click here

Pre-requisite: Vector calculus. Linear algebra. A fair level of mathematical maturity is expected.

Grades:  Homework (25%), Final Exam (50%), and Course Project (25%).

TA: Yuanxin Guo (yuanxin.guo@mail.utoronto.ca) and Yiming Liu (eceym.liu@mail.utoronto.ca) and Nick Kwan (nick.kwan@mail.utoronto.ca)

References:

• Dimitri P. Bertsekas, Nonlinear Programming, Athena Scientific, 1999.
• David G. Luenberger, Optimization by Vector Space Methods, Wiley, 1969.
• R. Tyrell Rockafellar, Convex Analysis, Princeton University Press, (available in a 1996 reprint).

Last Updated: March 19, 2025