Overview
This is an introductory course on convex and linear optimization. Topics include basics of mathematical optimization, convex sets and functions, convex and linear optimization problems, basic algorithms for convex optimization, optimality conditions for unconstrained and constrained optimizations, Lagrange duality.
Requirements: Coursework will include
 Homework assignments every 12 weeks, 50% of course grade.
 A final exam, 50% of course grade.
Grading policy:
 NO late homework submission will be accepted.
Honor code:
 You are encouraged to discuss homework assignments with each other, but write up solutions on your own! Sharing or copying a solution will result in a zero score for the relevant assignment for both parties.
 If a significant part of your solution is due to someone else or from other sources (books, forums, etc), you should acknowledge the source! Failure to do so will result in a zero score for the relevant assignment.
References
 [BV] Convex Optimization, by Boyd and Vandenberghe, available free here
 [CZ] An Introduction to Optimization, by Chong and Zak, 电子工业出版社（翻译版）
 [B] Nonlinear Programming, by Bertsekas, 3rd Edition, 清华大学出版社（英文影印版）
 [NW] Numerical Optimization, by Nocedal and Wright, 科学出版社
 [LY] Linear and Nonlinear Programming, by Luenberger and Ye, 3rd Edition, 世界图书出版公司（英文影印版）
Homeworks
 Homework 1. Released 9/14, due 9/21.
 Homework 2. Released 9/21, due 9/28.
 Homework 3. Released 9/29, due 10/12.
 Homework 4. Released 10/12, due 10/19.
 Homework 5. Released 10/19, due 10/26.
 Homework 6. Released 10/28, due 11/11.
 Homework 7. Released 11/2, due 11/9.
 Homework 8. Released 11/9, due 11/16.
 Homework 9. Released 11/16, due 11/23.
 Homework 10. Released 11/23, due 11/30.
 Homework 11. Released 11/30, due 12/7.
 Homework 12. Released 12/7, due 12/14.
 Homework 13. Released 12/14, due 12/23.
Lecture Schedule
The schedule may change as the semester progresses.
Week 
Date 
Lecture Topics 
Readings 
Assignments 
1 
9/7 
basics of mathematical optimization, examples, global and local minima 


2 
9/14 
first and secondorder conditions for unconstrained problems 

HW 1 out 
3 
9/21 
convex sets 

HW 1 due
HW 2 out

4 
9/28 
convex functions 

HW 2 due
HW 3 out

5 
10/5 
NO CLASS (rescheduled to 10/10) 
10/10 
more convex functions 


6 
10/12 
convexitypreserving operations, convex optimization problems

 Slides
 [BV] 3.2, 4.1 4.2.14.2.4, 4.34.3.1

HW 3 due
HW 4 out 
7 
10/19 
convex optimization problems 
 Slides
 [BV] 4.44.4.1, 4.54.5.3

HW 4 due
HW 5 out

8 
10/26 
gradient descent 

HW 5 due
HW 6 out

9 
11/2 
analysis of gradient descent, strong convexity, condition number 

HW 6 due
HW 7 out

10 
11/9 
line search, Newton's method 

HW 7 due
HW 8 out

11 
11/16 
analysis of Newton's method, damped Newton's method, equality constrained problems 

HW 8 due
HW 9 out

12 
11/23 
Lagrange multipliers method, Newton's method for equality constrained problems 

HW 9 due
HW 10 out

13 
11/30 
general equality constrained problems, inequality constrained problems and KKT conditions 

HW 10 due
HW 11 out 
14 
12/7 
more KKT conditions, Lagrange dual problems 

HW 11 due
HW 12 out 
15 
12/14 
weak and strong duality, Slater's condition, duality and KKT conditions 

HW 12 due
HW 13 out 
16 
12/21 
review 


