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 applications.

This graduate course introduces convex optimization theory and illustrates its use with many recent applications in signal processing, finance, machine learning, communication systems, networking, robust design, image processing, etc. The emphasis will be on i) the art of unveiling the hidden convexity of problems by appropriate manipulations, and ii) a proper characterization of the solution either analytically or algorithmically. The course follows a case-study approach by considering recent successful applications of convex optimization published within the last decade in top scientific journals.

Problems will be covered in areas of signal processing, finance, and machine learning such as portfolio optimization in finance, filter/beamforming design, classification methods, circuit design, robust designs under uncertainty, sparse optimization, low-rank optimization, image processing, 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%
Midterm:   20% (auditors too)
Final Project: 60%  (homeworks and midterm are required to be passed)

Course Schedule

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

Lecture Information

Lecture Time: Mon 18:00 – 20:50

Lecture Venue: TBD

Teaching Team

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

Email: palomar@ust.hk    Office: 2398 (Lifts 17/18)

Office hour : By email appointment

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

 

Course Summary:

Date Details