Course Syllabus

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ELEC5470 – Convex Optimization

Fall 2025-26, 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.
  • Daniel P. Palomar (2025). Portfolio Optimization: Theory and Application. Cambridge University Press. portfoliooptimizationbook.com

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% (auditors too)
Midterm:   20% (auditors too)
Class participation: 10%
Final Project: 50%  (requirement: pass grade in homework and midterm)

Course Schedule

Date Week Lect Topic
1-Sep   1   1 Introduction
  2 Theory: Convex sets and convex functions
8-Sep   2   3 Theory: Convex problems and taxonomy (LP, QP, SOCP, SDP, GP)
  4 Application: Filter design
15-Sep   3   5 Theory: Algorithms primer (Newton, IPM, BCD)
  6 Application: Disciplined convex programming - CVX
22-Sep   4   7 Theory: Lagrange duality and KKT conditions
  8 Application: Waterfilling solutions
29-Sep   5   9 Application: Markowitz portfolio optimization
10 Theory&Application: Geometric programming (GP)
6-Oct   6 11 Theory&Application: MM and SCA based algorithms
12 Application: Sparsity via l1-norm minimization
13-Oct 7 Midterm
20-Oct   8 13 Application: Risk parity portfolio in finance
14 Application: Sparse index tracking in finance
27-Oct   9 15 Application: Classification and SVM in machine learning
16 Application: Low-rank optimization problems (Netflix, video security)
3-Nov 10 17 Application: Robust optimization with applications
18 Application: Graph learning from data
10-Nov 11 19 Application: ML decoding via SDP relaxation
20 Application: Rank-constrained SDP and multiuser downlink beamforming
17-Nov 12 21

Theory: Primal/dual decomposition techniques with applications
22 Application: alternative decompositions for NUM in wired and wireless networks
24-Nov 13 23 Application: The Internet as a convex optimization problem
24 Application: The iterative waterfilling algorithm
25 TA tutorial 1: Application - Sparsity-based mid-price prediction on limit order book
26 TA tutorial 2: Application - Differentiable convex optimization

Lecture Information

Lecture Time: Mon 6pm – 8:50pm

Lecture Venue: Rm5560 (Lifts 27/28)

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: Arnau Vilella Piqué (avp@connect.ust.hk) and Jong Ho Ju (jjuaa@connect.ust.hk)

Course Summary:

Course Summary
Date Details Due