Course Syllabus

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ELEC5470/IEDA5470 - Convex Optimization

Fall 2022-23, 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. [pdf]
  • 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: 25% (auditors too)
Midterm:   15% (auditors too)
Class participation: 10%
Final Project: 50%  (requirement: pass grade in homework and midterm)

Course Schedule

Date Week Lect Topic
5-Sep   1   1 Introduction
  2 Theory: Convex sets and convex functions

15-Sep (Thu) Rm1103

  2   3 Theory: Convex problems and taxonomy (LP, QP, SOCP, SDP, GP)
  4 Application: Filter design
19-Sep   3   5 Theory: Algorithms primer (Newton, IPM, BCD)
  6 Application: Disciplined convex programming - CVX
26-Sep   4   7 Theory: Lagrange duality and KKT conditions
  8 Application: Waterfilling solutions
3-Oct   5   9 Application: Markowitz portfolio optimization
10 Theory&Application: Geometric programming (GP)
10-Oct   6 11 Theory&Application: MM and SCA based algorithms
12 Application: Sparsity via l1-norm minimization
17-Oct   7 - Midterm -
24-Oct  8 13 Application: Risk parity portfolio in finance
  14 Application: Sparse index tracking in finance
31-Oct   9 15 Application: Classification and SVM in machine learning
16 Application: Low-rank optimization problems (Netflix, video security)
7-Nov 10 17 Application: Robust optimization with applications
18 Application: Graph learning from data
14-Nov 19 Application: ML decoding via SDP relaxation
20 Application: Rank-constrained SDP and multiuser downlink beamforming
21-Nov 12 21

Theory: Primal/dual decomposition techniques with applications

Application: alternative decompositions for NUM in wired and wireless networks
22 Theory: ADMM
28-Nov 13 23 Application: The Internet as a convex optimization problem
24 Application: Online learning with applications to universal portfolio

Lecture Information

Lecture Time: Mon 18:00 – 20:50

Lecture Venue: Rm1410

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: Shengjie XIU (sxiu@connect.ust.hk) and Runhao SHI (rshiaf@connect.ust.hk)

Course Summary:

Date Details Due