Department of Electrical and Computer Engineering
University of Toronto
Spring 2018
Weekly Schedule
Week 
Topics 
Text Reference 
Assignments 
1/09 
Introduction; Motivating Example: Data Fitting. Basic Concepts: Vector Space, Norm, Vector Calculus, Linear Algebra. 
Chapter 1 Appendix A 

1/16 
Gradient and Hessian of functions. Functions of matrices. Convex Sets. 
Chapter 2 
Due Jan 30 
1/23 
Convex functions. Firstorder and Secondorder conditions for differentiable convex functions. Properties of Convex Functions. 
Chapter 3 

1/30 
Convex optimization problems. Local and global optimal solutions of convex optimization problems. 
Chapter 4 

2/6 
Linear Programming. Quadratic programming. Quadratically constrained quadratic programming. Secondorder cone programming. Robust linear programming. 
Chapter 4 
Due Feb 27 
2/13 
(class held during the reading week instead) 


2/20 
Leastsquare problems. Optimal control problem. Geometric programming. Semidefinite programming. SDP relaxation. 
Chapter 4 

2/27 
Theory: Lagrangian. Dual optimization problem. Duality gap. Slater’s condition. Sensitivity analysis. 
Chapter 5, Rockafellar: 

3/6 
Duals of LP. Economics and Pricing Interpretation. Saddle points. Game theory. Duality theory for minimax optimization. 
Chapter 5, Rockafellar: 
Due March 27 
3/13 
Duals of QP. Controllabilityobservability duality. Dual of $l_p$ optimization. Duality theory for optimization problem with generalized inequality. SDP relaxation. 
Chapter 5 

3/20 
Complementary slackness condition. KarushKuhnTucker (KKT) Conditions. Interpretation of the KKT condition. Regularity condition for local optimality. Generalized inequalities. 
Bertsekas 

3/27 
Algorithms: Descent methods. Newton's method. Equality Constrained Minimization. Infeasiblestart Newton's Method. Interiorpoint method for constrained optimization. 
Chapter 9, Chapter 10 Chapter 11 
Due April 10 
4/3 
Interpretation of Interiorpoint method via KKT condition. PrimalDual InteriorPoint Method. Generalized Inequality. Analytic Centering. Ellipsoid method. Subgradient method for nondifferentiable functions. Dual Decomposition. 
Chapter 11 

4/10 
Sequential quadratic programming. Coordinate descent. Integer programming problems. Sparse optimization. 


4/10 
Project Presentation in class. 

Project Report Due April 13 

Final Exam: TBD 


TA office hour: Monday 11am12pm BA2179; Thursday 23pm BA4164 
The above schedule is subject to change.
Last Update: 1/9/2018