ESE 6050, Spring 2024 – Modern Convex Optimization
Instructor: Nikolai Matni, Assistant Professor, ESE Department
TAs: Renukanandan (Nandan) Tumu, Brian Lee, Akhilesh Tumu, Anirudh Cowlagi, Siming He, Heyi Liu, Keshav Ramji
Lectures: Tu/Th 3:305:00pm ET in LRSM Auditorium.
Syllabus: ESE6050001
If you are trying to register for the class: follow the instructions here. Do not email me, I cannot help you!
Canvas: We will be using Canvas to manage class logistics. Please log in and register here.
Office hours
Course description
In this course, you will learn to recognize and solve convex optimization problems that arise in applications across engineering, statistics, operations research, and finance. Examples will be chosen to illustrate the breadth and power of convex optimization, ranging from systems and control theory, to estimation, data fitting, information theory, and machine learning. A tentative list, subject to change, of what we will cover includes: convex sets, functions, and optimization problems; the basics of convex analysis; leastsquares, linear and quadratic programs, semidefinite programs, minimax, extremal volume, and other problems; optimality conditions, duality theory, theorems of alternatives, and applications; interiorpoint algorithms for solving convex optimization problems, and their complexity analysis; applications to signal processing, statistics and machine learning, control, digital and analog circuit design, and finance.
Course objectives
to give students the tools and skills needed to identify convex optimization problems that arise in applications
to introduce the basic theory of convex optimization problems, concentrating on results that are useful in understanding, improving, and extending computational methods
to give students a deep and foundational understanding of how such problems are solved, and hands on experience in solving them
to give students the background needed to feel comfortable in applying these methods in their own research work and/or applications
About the Course
Prerequisites
This is a math intensive course. A solid foundation in linear algebra (at the level of Math 314), as well as comfort with analysis, probability, and statistics at an advanced undergraduate level is required. Familiarity with one of Matlab, Python, or Julia. Undergraduates need permission.
Intended audience
This course will benefit anyone who uses or will use scientific computation or optimization in engineering, statistics, signal processing, or related work (e.g., machine learning, finance). More specifically, convex optimization problems are likely to pop up in the work of people in the following departments and fields: Electrical Engineering (signal/image processing, communications, control), Aero/Astro Engineering (guidance, navigation, control, design), Mechanical & Civil Engineering (robotics, control, structural analysis), Computer Science (machine learning, robotics, computer graphics, algorithms & complexity, computer networking), & Operations Research (Wharton).
Schedule
The following schedule is tentative and subject to change.
Date  Topic  Reading  Homework 
Week 1 1/18  Logistics, Introduction  Chapter 1 Appendix A  Sign up for Canvas & Piazza 
Week 2 1/23, 1/25  Convex sets  Chapter 2  Homework 1 (due 2/09) 
Week 3 1/30, 2/01  Convex functions  Chapter 3  No new homework 
Week 4 2/06, 2/08  Convex optimization problems  Chapter 4  No new homework 
Week 5 2/13, 2/15  Convex optimization problems Duality  Chapter 4, 5  Homework 2 (due 03/01) 
Week 6 2/20 , 2/22  Duality  Chapter 5  No new homework 
Week 7 2/27, 2/29  Approximation and fitting  Chapter 6  No new homework 
Spring Break 3/05, 3/07  relax  have fun  Homework 3 (due 03/22) 
Week 8 3/12, 3/14  Statistical estimation  Chapter 7  No new homework 
Week 9 3/19, 3/21  Statistical Estimation Geometric problems  Chapters 7, 8  No new homework 
Week 10 3/26, 3/28  Geometric problems Numerical Linear Algebra Review  Chapter 8 Appendix C  Homework 4 (due 4/12) 
Week 11 4/02, 4/04  Unconstrained minimization  Chapter 9  No new homework 
Week 12 4/09, 4/11  Equality constrained minimization  Chapter 10  No new homework 
Week 13 4/16, 4/18  Interiorpoint methods  Chapter 11  Homework 5 (due 05/01) 
Week 14 4/23, 4/25  Advanced topic: TBD  TBD  No new homework 
Week 15 4/30  Advanced topic: TBD Conclusions  N/A  Takehome Final Exam 24hr window in May 68

Textbook
The textbook is Convex Optimization by Boyd and Vandenberghe, available online.
Additional optional resources that may prove useful include:
J. Renegar, A Mathematical View of Interior Point Methods for Convex Optimization, 1998
A. BenTal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, SIAM, 2001
D. Bertsekas, A. Nedic, and A Ozdaglar, Convex Analysis and Optimization , 2003
L. El Ghaoui's EE227BT Lecture Notes
Software
You will use one of CVX (Matlab), CVXPY (Python), or Convex.jl (Julia), to write simple scripts. We refer to CVX, CVXPY, and Convex.jl collectively as CVX*.
Grading
Homework (70%): there will be triweekly homework assignments, handed out on Tuesday, and three Fridays later by 5pm (except for the final assignment which will be due the last day of class). The homework assignments must be LateXed and submitted on Canvas via Gradescope. Please use this LaTeX template – we ask that you write out detailed and rigorous solutions. You will be given 5 free late days which you may use as you please throughout the semester, after which no late assignments will be accepted. You are allowed, even encouraged, to work on homework in small groups, but you must write up your own homework solutions and code to hand in – please indicate who you collaborated with on your assignments. Each homework problem will be graded on a scale of 04.
Final takehome exam (30%): there will be a 24 hour final takehome exam scheduled during the final exam period. Please refer to the Stanford EE364a offering of this course for an idea of what the final exam will look like, as well as the logistics of how it will be administered.
Note that these weights are approximate, and we reserve the right to change them later.
Code of Academic Integrity: All students are expected to adhere to the University’s Code of Academic Integrity.
