MATH4230 - Optimization Theory - 2021/22

Announcement

• Course Outline [Download file]
• There will be no tutorial class in the first week.
• Zoom Link: https://cuhk.zoom.us/j/94379471220
• Please log in with your full name and department. Otherwise you could be kicked out.
• The midterm will be held on 15 March (Tue), covering everything up to Section 10.
• Project Specification [Download file]

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General Information

Lecturer

• Prof. Zeng Tieyong
  • Email:

Teaching Assistant

• Wong Hok Shing
  • Email:

Time and Venue

• Lecture: Tue 2:30pm - 4:15pm (Wu Ho Man Yuen 407); Wed 1:30pm - 2:15pm (Y.C. Liang Hall G04)
• Tutorial: Wed 12:30pm - 1:15pm (Y.C. Liang Hall G04)

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.
• Optima and Equilibria: An Introduction to Nonlinear Analysis (Graduate Texts in Mathematics, 140) 1998 by Jean-Pierre Aubin

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
• Lagrange duality and Examples
• Convex Optimization: Theory, Algorithms, and Applications (for reading)
• cuhk-notes-2022 (April 19, 2022)

Lecture Notes

• 1. Convex analysis (Ecole Polytechnique 2014)
• 2. Convex Optimization (UIUC)
• 3. Convex Optimization: Theory, Algorithms, and Applications (Gatech 2021)
• 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
• Note 10
• Note 11

Assignments

• Exercise 1
• Exercise 2
• Exercise 3
• Exercise 4
• Exercise 5
• Exercise 6
• Exercise 7
• Exercise 8
• Exercise 9
• Exercise 10
• Exercise 11

Solutions

• Solution 1
• Solution 2
• Solution 3
• Solution 4
• Solution 5
• Solution 6
• Solution 7
• Solution 8
• Solution 9
• Solution 10
• Solution 11

Useful Links

• Convex Optimization 2008 of illinois
• Convex Optimization (Book Stanford)
• Convex Optimization(Georgia Tech 2021)
• CONVEX ANALYSIS: An introduction to convexity and nonsmooth analysis
• An Easy Path to Convex Analysis and Applications
• Convex Optimization in Normed Spaces (2014)
• Convex analysis (Ecole Polytechnique)

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: April 19, 2022 23:52:57