MATH4230 - Optimization Theory - 2020/21

Announcement

• Course Outline [Download file]
• Zoom Link: https://cuhk.zoom.us/j/94379471220
• Please log in with your full name and department. Otherwise you could be kicked out.
• This is no Tutorial on Wednesday, Jan 13, 2020.
• Arrangements for Online Classes and Online Examinations : Unless otherwise advised by the course teachers concerned with alternative arrangements, all online classes and online examinations will continue as scheduled under any weather conditions, including when Tropical Cyclone Warning Signal No. 8 or above and/or Black Rainstorm Signal is hoisted.
• The midterm will be held online on 2 March (Tue), 14:30-15:45 (HKT)
• The deadline for the submission of report is 1 April, 23:59 (HKT)
• Project Specification [Download file]

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General Information

Lecturer

• Prof. Zeng Tieyong
  • Email:

Teaching Assistant

• Wong Hok Shing
  • Email:
• Yuxiang Hui
  • Email:

Time and Venue

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

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

• Boris S. Mordukhovich, Nguyen Mau Nam An Easy Path to Convex Analysis and Applications, 2013
• D. Michael Patriksson, An Introduction to Continuous Optimization: Foundations and Fundamental Algorithms, Third Edition (Dover Books on Mathematics), 2020
• D. Bertsekas, Convex Optimization Theory, Athena Scientific, 2009.

References

• 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 Algorithms, Athena Scientific, 2015.

Pre-class Notes

• Convex optimization prequisites review, by Nicole Rafidi
• Basic properties of limsup and liminf
• cuhk-notes-2021 (March 23, 2021)
• Video (March 24, 2021)

Lecture Notes

• Convex analysis (Ecole Polytechnique 2014)
• 1. Convex Optimization (UIUC)
• 2. Convex Optimization: Fall 2019 (CMU,with permission)
• 3. Convex Optimization, Spring 2017, Notes (Gatech)
• Notes of Stanford
• Proximal-ADMM(wen zaiwen)
• Notes for Newton’s Method for Unconstrained Optimization (MIT)
• Notes for subdifferential calculus
• ADMM
• ADMM
• Notes of MIT (with permission)
• Notes of Nemirovski (with permission)
• old-Lecture notes of CUHK

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
• Nonvertical separation

Tutorial Notes

• Note 1
• Note 2
• Note 3
• Note 4
• Note 5
• Note 6
• Note 7
• Note 8
• Note 9

Assignments

• Exercise 1
• Exercise 2
• Exercise 3
• Exercise 4
• Exercise 5
• Exercise 6
• Exercise 7
• Exercise 8
• Exercise 9

Solutions

• Solution 1
• Solution 2
• Solution 3
• Solution 4
• Solution 5
• Solution 6
• Solution 7
• Solution 8

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.

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Assessment Policy

Last updated: March 24, 2021 14:12:28