Course Syllabus

ELEC5470/IEDA6100A - Convex Optimization

Fall 2019-20, HKUST

Description

In the last three decades, a number of fundamental and practical results have been obtained in the area of convex optimization theory. It is a well-developed area, both in the theoretical and practical aspects, and the engineering community has greatly benefited from these recent advances by finding key applications.

This graduate course introduces convex optimization theory and illustrates its use with many applications where convex and nonconvex formulations arise. The emphasis will be on i) the art of unveiling the hidden convexity of problems by appropriate manipulations, ii) a proper characterization of the solution either analytically or algorithmically, and iii) multiple practical ways to approach nonconvex problems.

The course follows a case-study approach by considering recent successful applications of convex optimization published within the last decade in top scientific journals in the areas of signal processing, finance, machine learning, and big data. Problems covered include portfolio optimization in financial markets, filter design, beamforming design in wireless communications, classification in machine learning, circuit design, robust designs under uncertainty, sparse optimization, low-rank optimization, graph learning from data, discrete maximum likelihood decoding, network optimization, distributed algorithms, Internet protocol design, etc.

Textbooks

  • Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.[https://web.stanford.edu/~boyd/cvxbook]
  • Daniel P. Palomar and Yonina C. Eldar, Convex Optimization in Signal Processing and Communications, Cambridge University Press, 2009.

Prerequisites

Students are expected to have a solid background in linear algebra. They are also expected to have research experience in their particular area and be capable of reading and dissecting scientific papers.

Grading

Homework: 20% (including auditors)
Midterm:   20% (including auditors)
Final Project: 60%  (homeworks and midterm are required to be passed)

Course Schedule

Date Week Lect Topic
9-Sep   1   1 Introduction
  2 Theory: Convex sets and convex functions
16-Sep   2   3 Theory: Convex problems and taxonomy (LP, QP, SOCP, SDP, GP)
  4 Application: Filter design
23-Sep   3   5 Theory: Numerical algorithms – interior point method
  6 Theory: Disciplined convex programming - CVX
30-Sep   4   7 Theory: Lagrange duality and KKT conditions
  8 Application: Waterfilling solutions
14-Oct   5   9 Application: Markowitz portfolio optimization
10 Theory&Application: MM-based algorithms
21-Oct   6 11 Application: Risk parity portfolio in finance
12 Theory&Application: Geometric programming (GP)
28-Oct   7 13 Application: Sparsity via l1-norm minimization
14 Application: Sparse index tracking in finance
4-Nov   8 - Midterm -
6pm-9pm   18-Nov  Rm5508   9 15 Application: Classification and SVM in machine learning
16 Application: Low-rank optimization problems (Netflix, video security)
3-4:30pm  20-Nov  Rm4621 10 17 Application: Robust optimization with applications
3-4:30pm  22-Nov  Rm4621 18 Application: Graph learning from data
6pm-9pm    25-Nov  Rm5508 11 19 Application: ML decoding via SDP relaxation
20 Application: Rank-constrained SDP and multiuser downlink beamforming
3-4:30pm  27-Nov  Rm4621 12 21 Theory: primal/dual decomposition techniques
3-4:30pm  29-Nov  Rm4621 22 Application: The Internet as a convex optimization problem

Lecture Information

Lecture Time: Mon 18:00 – 20:50

Lecture Venue: CYTG009A (next to Subway)

Teaching Team

Instructor: Prof. Daniel P. PALOMAR (https://www.danielppalomar.com)

Email: palomar@ust.hk    

Office: 2398 (Lifts 17/18)

Office hours: By email appointment

TAs: Jiaxi YING (jx.ying@connect.ust.hk) and Irtaza KHAN (iakhan@connect.ust.hk)

 

Course Summary:

Date Details