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]
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 quasiNewton 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 JeanPierre 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.
Preclass 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)
 cuhknotes2022 (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
 ProximalADMM(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)
 oldLecture notes of CUHK
Class Notes
 Convex sets, and Convex FunctionsJan82020
 Convexity and Continuity (Jan152020)
 Convex functions (Feb182020)
 Gradient method (Feb192020)
 Fenchel Conjugate (Feb 252020)
 subgradientzeng (Feb 262020)
 SeparationthmSubgradients (March 42020)
 GradientDualityKKT (March 10112020,updated)
 More on KKT (March 172020)
 Lagrange duality and Examples (March 242020)
 Proximal Algorithms (April 72020)
 Proximal Gradient Algorithms (April 782020)
 Fast proximal gradient methods (April 14152020)
 ADMM with proof (revised April 21222020)
 More on ADMM (April 282020)
 Newton’s method
 Proximal Algorithms
 Duality and KTT
 KarushKuhnTucker conditions
 Perspective function(Jan82020)
 Caratheodory’s Theorem (Jan142020)
 Existence of Solutions and Optimality Conditions
 Conjugate functions
 Primal and dual problems
 Gradient descent
 Subgradients
 subgradients
 MatrixLasso (April 82020)
 Weak Duality
 Strong Duality
 Newton’s method
 Nonvertical separation
Tutorial Notes
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.
Assessment Policy Last updated: April 19, 2022 23:52:57