MATH4230 - Optimization Theory - 2023/24

Announcement

• The mid-term will be on March 12, 2024, Tuesday.
• The mini-project is released on Blackboard. You may form a group of at most 2 students and hand in a report of length between 5 and 10 pages before 2024/4/13, 11:59 pm.

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General Information

Lecturer

• Zeng Tieyong
  • Office: LSB 225
  • Tel: (852) 3943-7966
  • Email:

Teaching Assistant

• Zeyu Li
  • Office: LSB 222A
  • Tel: 3943 3575
  • Email:
• Shengze Xu
  • Office: LSB 222C
  • Tel: 3943 8570
  • Email:

Time and Venue

• Lecture: Tu 14:30 - 16:15 ( Mong Man Wai Bldg 703); We 14:30 - 15:15 (Science Centre L3)
• Tutorial: We 15:30 - 16:15 (Science Centre L3)

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

• G. Lan, First-order and Stochastic Optimization Methods for Machine Learning, Spriner 2020.
• 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.
• Boris S. Mordukhovich, Nguyen Mau Nam An Easy Path to Convex Analysis and Applications, 2013.

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.

Lecture Notes

• Note 1 (For course)
• Note 2 (For reference)
• Note 3 (For tutorial)

Class Notes

• Introduction to optimization-Jan9, 2024
• Mathematical review-Jan 16, 2024
• Convex function-Feb 6, 2024
• Subgradient-Feb 14, 2024
• Moreau-Rockafellar Thm-Feb 28, 2024
• Support Vector Machines-March 26, 2024
• KKT condition-April 2, 2024
• Normal cone
• Conjugate functions-April 10, 2024
• Gradient descent -April 16, 2024

Tutorial Notes

• Convex Set
• Relative Interior
• Convex Function
• Conjugate Function
• Subgradient
• Lipschitz Continuous
• KKT Condition
• Fenchel Conjugate

Assignments

• Assignment 1
• Assignment 2
• Assignment 3
• Assignment 4
• Assignment 5
• Assignment 6
• Assignment 7
• Assignment 8
• Assignment 9
• Assignment 10

Solutions

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

Assessment Scheme

Tutorial attendance & good efforts or top 15% in both the mid- and final exams (tutorial assignments are counted only if they are submitted before 6:30pm Monday next after the tutorial class)		10%
Mid-Exam		17.5%
Mini-Project		17.5%
Final-Exam		55%

Useful Links

• Convex Optimization 2008 of illinois
• Convex Optimization (Book Stanford)
• Convex Optimization(Georgia Tech 2022)
• CONVEX ANALYSIS: An introduction to convexity and nonsmooth analysis
• An Easy Path to Convex Analysis and Applications
• 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 16, 2024 12:36:10