MATH4230 - Optimization Theory - 2019/20
Announcement
- Course Outline [Download file]
- There will be no tutorial class in the first week.
- Project Specification [Download file]
- The midterm will be held online on 25 March (Wed), 13:00-13:45
- There will be no final exam. The following assessment scheme will be adopted: Exercise: 20%, Midterm: 30%, Project: 50%
- The deadline for the submission of report will be postponed to 11 May, 23:59 (HKT)
- No class during Reading Week
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, 2013
- D. Bertsekas, Convex Optimization Algorithms, Athena Scientific, 2015.
Pre-class Notes
- Convex optimization prequisites review, by Nicole Rafidi
- Nonvertical separation
- Basic properties of limsup and liminf
Lecture Notes
- Lecture notes of CUHK
- Convex Optimization: Fall 2019 (CMU,with permission)
- Notes of MIT (with permission)
- Notes of Nemirovski (with permission)
- Notes of Stanford
- Convex Optimization (UIUC)
- Convex Optimization, Spring 2017, Notes (Gatech)
- Proximal-ADMM(wen zaiwen)
- Notes for Newton’s Method for Unconstrained Optimization (MIT)
- Notes for subdifferential calculus
- ADMM
- ADMM
Class Notes
- Convex sets, and Convex Functions-Jan8-2020
- Convexity and Continuity (Jan15-2020)
- Convex functions (Feb18-2020)
- Gradient method (Feb19-2020)
- Fenchel Conjugate (Feb 25-2020)
- subgradient-zeng (Feb 26-2020)
- Separationthm-Subgradients (March 4-2020)
- Gradient-Duality-KKT (March 10-11-2020,updated)
- More on KKT (March 17-2020)
- Lagrange duality and Examples (March 24-2020)
- Proximal Algorithms (April 7-2020)
- Proximal Gradient Algorithms (April 7-8-2020)
- Fast proximal gradient methods (April 14-15-2020)
- ADMM with proof (revised April 21-22-2020)
- More on ADMM (April 28-2020)
- Newton’s method
- Proximal Algorithms
- Duality and KTT
- Karush-Kuhn-Tucker conditions
- Perspective function(Jan8-2020)
- Caratheodory’s Theorem (Jan14-2020)
- Existence of Solutions and Optimality Conditions
- Conjugate functions
- Primal and dual problems
- Gradient descent
- Subgradients
- subgradients
- Matrix-Lasso (April 8-2020)
- Weak Duality
- Strong Duality
- Newton’s method
Tutorial Notes
Assignments
- Exercise 1
- Exercise 2 (Q3 Modified)
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Exercise 9
- Exercise 10
Solutions
- Solution 1
- Solution 2
- Solution 3
- Solution 4
- Solution 5
- Solution 6
- Solution 7
- Solution 8
- Solution 9
- Solution 10
Useful Links
- Convex Optimization 2008 of illinois
- Convex Optimization (Book Stanford)
- Convex Optimization(Georgia Tech 2017)
- Convex Optimization(CMU Fall 2019)
- An Easy Path to Convex Analysis and Applications
- Convex Optimization in Normed Spaces (2014)
- Convex analysis (Ecole Polytechnique)
- CONVEX ANALYSIS: An introduction to convexity and nonsmooth analysis
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:
http://www.cuhk.edu.hk/policy/academichonesty/and thereby help avoid any practice that would not be acceptable.
Assessment Policy Last updated: January 04, 2021 10:35:00