Syllabus

Week 1 (1-Sep-2025)

Lecture 1: Introduction
Slides: intro
Reading assignment: Appendix A.1 in the book portfoliooptimizationbook.com

Lecture 2: Theory: Convex sets and convex functions
Slides: Sections 2-3 in convex optimization theory
Reading assignment: Appendices A.2-A.3 in the book portfoliooptimizationbook.com (For more details, see Chapters 2 and 3 of B&V textbook. For mathematical background, see Appendix A of B&V textbook.)

Week 2 (8-Sep-2025)

Lecture 3: Theory: convex problems and taxonomy (LP, QP, SOCP, SDP, GP)
Slides: Sections 4, 5, and 7 convex optimization theory
Reading assignment: Appendices A.4-A.5, A.7 in the book portfoliooptimizationbook.com (For more details, see Chapter 4 of B&V textbook.)
Homework: HW#1 (due 15-Sep).

Lecture 4: Application: filter design
Slides: filter design
Reading assignment: SPM 2010 tutorial by Davidson (optional: paper on antenna array pattern synthesis by Lebret&Boyd).

Week 3 (15-Sep-2025)

Lecture 5: Theory: Algorithms primer (Newton, IPM, BCD)
Slides: Sections 2, 3, 5 in optimization algorithms
Reading assignment: Appendices B.2-B.4, B.6 in the book portfoliooptimizationbook.com (for more details, see Chapters 9 and 11 of B&V textbook).

Lecture 6: Application: disciplined convex programming - cvx
Slides: Section 1 in optimization algorithms
Reading assignment: Appendix B.1 in the book portfoliooptimizationbook.com and cvx user guide.

Homework: HW#2. You can use different programming languages like:
Matlab (cvx package)
Python (cvx package)
R (cvx package)
Julia (cvx package)

Week 4 (22-Sep-2025)

Lecture 7: Theory: Lagrange duality and KKT conditions
Lecture notes: Section 6 in convex optimization theory
Reading assignment (optional): Appendix A.6 in the book portfoliooptimizationbook.com (for more details, see Chapter 5 of B&V textbook), historical note by Kuhn

Lecture 8: Application: waterfilling solutions
Lecture notes: whiteboard and slides-vector-water-filling
Reading assignment: paper on iterative waterfilling by Yu, Rhee&Cioffi

Homework: HW#3 (due before next class).

Week 5 (29-Sep-2025)

Lecture 9: Application: Markowitz Portfolio Optimization
Lecture notes: Markowitz portfolio
Reading assignment: Chapters 6-7 in the book portfoliooptimizationbook.com, paper general mean-variance optimization

Lecture 10: Theory&Application: Geometric Programming (GP)
Lecture notes: GP with applications in power control
Reading assignment: GP tutorial by Boyd et al., paper on power control via GP

Week 6 (6-Oct-2025)

Lecture 11: Theory&Application: Algorithms - MM and SCA
Lecture notes: Sections 6-7 in optimization algorithms
Reading material: Appendices B7-B.8 in the book portfoliooptimizationbook.com, 2017 MM tutorial, 2014 SCA paper

Lecture 12: Application: Sparsity via Convex Optimization
Lecture notes: Sparsity via convex optimization
Reading material: SPM 2010 tutorial by Zibulevsky&Elad

Week 7 - Midterm (13-Oct-2025)

Week 8 (20-Oct-2025)

Lecture 13: Application - Risk parity portfolio in finance
Lecture notes: risk parity portfolio
Reading material: Chapter 11 in the book portfoliooptimizationbook.com

Lecture 14: Application - Sparse index tracking in finance
Lecture notes: index tracking
Reading material: Chapter 13 in the book portfoliooptimizationbook.com

Week 9 (27-Oct-2025)

Lecture 15: Application – classification and SVM
Lecture notes: SVM
Reading material: application paper by Vapnik'99

Lecture 16: Application – low-rank optimization problems (e.g., Netflix, video security)
Lecture notes: low-rank matrix optimization

Week 10 (3-Nov-2025)

Lecture 17: Application – Robust optimization with applications
Lecture notes: robust optimization

Lecture 18: Application – Graph learning from data
Lecture notes: graph learning

Week 11 (10-Nov-2025)

Lecture 19: Application – ML decoding via SDP relaxation
Lecture notes: SDP relaxation for ML decoding

Lecture 20: Application – Rank-constrained SDP and multiuser downlink beamforming
Lecture notes: rank-constrained SDP

Week 12 (17-Nov-2025)

Lecture 21: Theory – primal/dual decomposition techniques and ADMM
Lecture notes: primal-dual decompositions, ADMM
Reading material: Appendix B in the book portfoliooptimizationbook.com (Section B.9 for ADMM)

Lecture 22: Application – primal/dual decomposition techniques and ADMM
Lecture notes: alternative decompositions for NUM in wired and wireless networks
Reading material: tutorial paper by Palomar&Chiang, more detailed paper by Palomar&Chiang

Week 13 (24-Nov-2025)

Lecture 23: Application – The Internet as a convex optimization problem
Lecture notes: optimizing the Internet

Lecture 24: Application – The iterative waterfilling algorithm
Lecture notes: iterative waterfilling

TA tutorial 1: Application - Sparsity-based mid-price prediction on limit order book
Tutorial notes: sparse lob prediction

TA tutorial 2: Application - Differentiable convex optimization
Tutorial notes: differentiable convex optimization