G00TE1204: Convex Optimization and Its Applications in Signal Processing

School of Telecommunications Engineering
Xidian University

Announcements

NEW: Here is a supplementary handout on SDP rank reduction.
Homework 4 is posted. It is due on June 11, 2015.
Welcome to the course!

General Information

Instructor: Anthony Man-Cho So (manchoso at se.cuhk.edu.hk)
Lecture Time: Tuesdays, Wednesdays 2:30pm - 5:15pm

Teaching Assistants:
- TBA

Course Description

In this course we will develop the basic machineries for formulating and analyzing various optimization problems. Topics include convex analysis, linear and conic linear programming, nonlinear programming, optimality conditions, Lagrangian duality theory, and basics of optimization algorithms. Applications from different fields, such as combinatorial optimization, communications, computational economics and finance, machine learning, and signal and image processing, will be used to complement the theoretical developments. No prior optimization background is required for this class. However, students should have workable knowledge in multivariable calculus, real analysis, linear algebra and matrix theory.

Course Requirements

4-5 homework sets (60%) and an in-class final examination (40%).

General References

Ben-Tal, Nemirovski: Optimization I-II: Convex Analysis, Nonlinear Programming Theory, Nonlinear Programming Algorithms, 2004.
Boyd, Vandenberghe: Convex Optimization, Cambridge University Press, 2004.
Cottle: Lecture Notes on Optimization, 2004.
Güler: Foundations of Optimization, Springer, 2010.
Luenberger, Ye: Linear and Nonlinear Programming (3rd Edition), Springer, 2008.
Nemirovski: Lectures on Modern Convex Optimization, 2005.

Handouts

Handout A: Linear Algebra Cheat Sheet
Handout B: Real Analysis Cheat Sheet

The mathematical prerequisites for this course are summarized in Handouts A and B. Students are strongly advised to go through them carefully.
Handout 1: Introduction
Handout 2: Elements of Convex Analysis
Handout 3: Elements of Linear Programming
Handout 4: Some Applications of Linear Programming
Handout 5: Elements of Conic Linear Programming
Handout 6: Some Applications of Conic Linear Programming (Supplement)
Handout 7: Optimality Conditions
Handout 8: Optimality Conditions and Lagrangian Duality

Homework Sets

Homework 1 (due May 21, 2015) Solution
Homework 2 (due May 28, 2015) Solution
Homework 3 (due June 4, 2015) Solution
Homework 4 (due June 11, 2015)

Last Updated: June 20, 2015