Announcement

• Course Outline [Download file]
• There will be no tutorial class in the first week.
• Midterm will be held at LSB LT4,1-2PM on Mar 6
• Project Specification [Download file]
• Final Exam : 7 May (Tue), 15:30-17:30, Sir Run Run Shaw Hall(Auditorium)

General Information

Lecturer

• Prof. Zeng Tieyong
  • Email:

Teaching Assistant

• Wong Hok Shing
  • Email:

Time and Venue

• Lecture: Tue 2:30pm - 4:15pm, LSB LT4; 1:30pm - 2:15pm, LSB LT4
• Tutorial: Wed 12:30pm - 1:15pm, LSB LT4

Course Description

Unconstrained and equality optimization models, constrained problems, optimality conditions for constrained extrema, convex sets and functions, duality in nonlinear convex programming, descent methods, conjugate direction methods and quasi-Newton methods. Students taking this course are expected to have knowledge in advanced calculus.

Textbooks

• S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
• D. Bertsekas, A. Nedic, A. Ozdaglar, Convex Analysis and Optimization, Athena Scientific, 2003.
• D. Bertsekas, Convex Optimization Theory, Athena Scientific, 2009.
• Boris S. Mordukhovich, Nguyen Mau Nam An Easy Path to Convex Analysis and Applications, 2014

Pre-class Notes

• Basic properties of limsup and liminf
• Nonvertical separation

Lecture Notes

• Notes of Stanford
• Notes of Nemirovski (with permission)
• Notes of MIT (with permission)
• Notes for Newton’s Method for Unconstrained Optimization (MIT)
• Notes for subdifferential calculus
• ADMM
• ADMM
• Proximal-ADMM(wen zaiwen)

Class Notes

• Convex sets, and Convex Functions
• Convexity and Continuity
• Conjugate functions
• Existence of Solutions and Optimality Conditions
• Gradient descent
• Primal and dual problems
• Subgradients
• Gradient method
• Subgradients
• subgradients
• Karush-Kuhn-Tucker conditions
• Duality and KTT
• Weak Duality
• Strong Duality
• Newton’s method
• Newton’s method
• Proximal Algorithms
• Proximal Algorithms
• Proximal Gradient Algorithms

Tutorial Notes

• Proof of Caratheodory's Theorem
• Convex Function
• Conjugate Function
• Relative interior
• Optimal conditions
• Moreau-Rockafellar Theorem
• Normal Cone
• Gradient descent
• ADMM

Assignments

• Exercise 1
• Exercise 2
• Exercise 3
• Exercise 4
• Exercise 5 (3b modified)
• Exercise 6
• Exercise 7
• Exercise 8
• Exercise 9
• Exercise 10

Solutions

• Exercise 1 Solution
• Exercise 2 Solution
• Exercise 3 Solution
• Exercise 4 Solution
• Exercise 5 Solution
• Exercise 6 Solution
• Midterm Solution
• Exercise 7 Solution
• Exercise 8 Solution
• Exercise 9 Solution
• Exercise 10 Solution

Useful Links

• Convex Optimization 2008 of illinois
• Convex Optimization (Book Stanford)
• Convex Optimization(Georgia Tech 2017)
• Convex Optimization(CMU Fall 2015)
• An Easy Path to Convex Analysis and Applications
• Convex Optimization in Normed Spaces (2014)

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

and thereby help avoid any practice that would not be acceptable.